I think most of it has been explained throughout the thread but I'll chime in anyway with my understanding. If I'm missing anything or if any info is slightly off then feel free to chime in and correct me.
To understand the issue you have to go back to the Megadrive days. Sega Japan and Sega America were trying to compete too much internally and what was good for one market didn't necessarily fly in the other market.
Sega Japan had only moderate success with the Megadrive in Japan, it wasn't an out and out failure, but it certainly wasn't lighting up the charts compared to the NES and SNES. At the same time through clever marketing and the right content/market conditions Sega America were a runaway success becoming the market leader for a period ahead of the mighty Nintendo who were unstoppable in Japan.
This led to a lot of clashing egos on both sides with the Japan branch being sour for being compared non favourably to the highly successful American arm and the American arm feeling like they knew what was best and that they should be calling all of the shots.
This led to internal bickering much of which we likely only hear bits of pieces of now. Rather than working together as a team and doing what's best for the overall company by combining strengths the two branches instead tried to one up each other and compete for brownie points with the top brass.
So coming up towards the Saturn this internal strife and wasting of talent resources came up again. The Mega CD was an experiment which Sega can't really be blamed for as FMV/CD was all the rage at the time and even Nintendo were also working on their own disc drive add on which we all know about but had it released would probably have been as unsuccessful as the Mega CD was.
The American branch believed that they found success with the Megadrive so expanding it's life span with the 32X was the right idea rather than putting all resources into the next console. This obviously was a failure and combined with the Mega CD customers had begun to lose a bit of faith in Sega's direction as a company and brand.
The Japanese branch having been pioneers in 3D graphics in gaming from their highly successful arcade business should have been well in the lead in the R&D/Talent department and their next console should have been a smash hit in terms of wow factor and technology.
However a lack of foresight and a bad read on marketing conditions led the Japanese branch to the thinking that they wanted to maintain a tiered environment where arcades possessed the best technology and gave you that "WOW" factor and home consoles were more simplistic. I suppose you could say the thinking was likely akin to the Cinema experience verses the home video experience at the time.
There was likely an element of not wanting to cannibalise Sega's at the time highly successful arcade business and probably also more egos clashing between say the arcade division and the home console division.
So Sega Japan set out to make a machine that continued advancing 2D graphics assuming everyone else would go the same route and leave fancy 3D tech to the arcades.
Later when Sega realised that everyone else was going the 3D home console route they had to scramble to get the Saturn together causing a mish-mash of design philosophies and chipsets which made the Saturn highly difficult to develop for and although a 2D powerhouse from it's initial design philosophy the console's 3D capabilities were somewhat lacking and certainly a late addition in the development cycle.
But Sega had done their research, at least as far as the Japanese market was concerned and had deals in the works with several Japanese third parties who had only recently been freed from Nintendo's draconian monopoly contracts and wanted to work with someone else.
The Saturn released in Japan and was a huge success over there compared to the Megadrive. The Saturn was going toe to toe with the Playstation for the first year. The Japan branch finally felt they were successful by tailoring everything to what they knew of the Japanese market. This however was in stark contrast to the western release of the Saturn.
The Japan branch decided that because the Megadrive was only moderately successful for them that it was better to put past failures behind them and concentrate all their eggs in the next gen basket so all production on Megadrive games was halted. This may have been good for the Japanese market but not for the US market where the Megadrive was still a huge success. This in the US market was a huge blow to Sega as a company as they were killing off the golden goose as it were and stopping that revenue stream and consumer mindshare.
The Sony Playstation was on the horizon and Sony had been wining and dining developers and publishers to bring software to their platform, and they were doing a great job of it too. Backed by the branding and worldwide success/money of Sony which was an unstoppable brand at the time serious competition was on the way.
In what can only be described as one of the dumbest moves in videogame history the Saturn was launched in the US months early to compete with the Sony Playstation in the strangest stealth launch ever. It was a total rush job with no marketing to back it up yet and almost no software as third parties were still working on their launch titles for the console.
This understandably pissed off everyone: publishers, developers, marketing departments, retailers and consumers.
For consumers especially this was the last straw, coming off the back of the Mega CD and 32X failures, the sudden forced death of the Megadrive and now this stealth launch of the Saturn with barely any software or marketing and no mascot Sonic game anywhere in the pipeline.
The Saturn unsurprisingly failed in the west....hard. The Japan branch had finally started to gain success in it's home territory but all for nothing as their decisions had led to the doom of their own brand/console in the rest of the world. Had things been different and better decisions made in final days of the Megadrive and the lead up to the Saturn then we could be living a very different history now but alas Sega had the ball and dropped it so hard it won't likely ever be forgotten.
So coming off the death of the Megadrive and the costly R&D on it's failed add ons. The failure of the Saturn and the sudden decline of the arcades Sega had pretty much lost all of it's revenue streams in just a few shorts years. The company had lost the faith of consumers and publishers alike and was in financial ruin essentially.
But desperate to regain their success and become a competitor again Sega set to work on the Dreamcast, this time they would finally learn from their mistakes and both branches would work together for the common good.
They borrowed money and got to work on a fantastic console. Learning from the terrible launch of the Saturn the Dreamcast had software coming out of it's ears for the launch and first 18 months. It was very front loaded but it needed to be to make an impact.
And to it's credit despite everything against it, the Dreamcast was pretty successful for a time, but it needed to be an absolute runaway success. The console was perfectly aimed at the hardcore and normally were it around longer the mainstream would eventually jump in too, however this was not the case with the Dreamcast.
The Playstation had been an unprecedented success and brought in gamers from much wider age ranges. Games were no longer for little kids, the mainstream were involved now. The hype for the Playstation 2 was bigger than anything before or since. It was simply monumental, and the marketing both backed and played to this fact. The public mindshare was with Sony now and nothing Sega could do would change this. When combined with the high demand and price of DVD players Sony pulled an amazing move and people were using PS2 as a cheap DVD player too further increasing it's success.
Sega had pretty much ran out of money at this stage, if they had a war chest like what Nintendo does it's possible the Dreamcast could have carved out a reasonable success in the market but there just wasn't anymore money coming through the pipeline.
There were talks with Microsoft to buy Sega which almost happened, and Sega knew that afterwards Microsoft were coming to market with or without them. Given the market conditions of high spenders Microsoft and Sony in the market with longterm darling Nintendo and a broke Sega the writing was on the wall.
The Dreamcast itself didn't fail Sega, Sega failed the Dreamcast to put it bluntly. Had "Dreamcast era" Sega been around since the middle of the Megadrive things would have been completely different but they squandered every lead they had by being Sega up to that point essentially and let a competitor take the market they had helped to foster right out from under them. They ran out of money and the public/industry ran out of faith in them.