The Logitech K400
Tried different USB ports? I don't suppose there's another PC you could test the keyboard and mouse on? They both come with Unifying receivers, so you've tried both receivers and both have the same problem?
Any wifi networks nearby? As I understand it, the Unifying receiver works on the 2.4GHz band which is shared by wifi devices and some types of cordless phones.
Just bought a ASUS GTX980 that came with download of Witcher 3. It'll be GTAV for a month than on to that. Going from a Radeon 7800. Putting it right in with AMD FX 8350 B.E. and 8 GB of ram.
My big Q is how long will my CPU be great for? What if I want to update my monitor in a year to 2560 x 1440?
Are you overclocking your processor? That will help extend its useful life. Honestly it'll depend on the game, as some games benefit more from CPU than GPU and vice versa. Although your FX-8350 isn't bad, at stock speed it's not on par with an Intel i5 in most cases.