Hmm. I'd try doing another install, going through the directions BGratz gave you in the order they gave them to you. Something was weird the first time you did it, because if it was a fully fresh install, it wouldn't have had a "current character" for you to try logging into. Something saved, got redownloaded, or simply didn't get deleted in the first place.

So if it was there, then you didn't delete everything out of the folder. If you had mods, they are also probably still there, and that's VERY LIKELY to be the problem.

Once you've got it all uninstalled and before you've gone through adding any of it back, make sure you go into the folder and manually delete any traces of the game. This step (or just renaming this folder) is REALLY important.

Turn off steam cloud if you haven't, yet.

If none of the above assists, do what you can to troubleshoot your hardware to make sure something isn't on its way out. There's any number of things that could be acting up and causing the described symptoms. Yes, a hardware failure can indeed manifest in only one game (particularly near the start of the problem), because different programs use different parts of the computer in different ways.