Admittedly, this issue is currently affecting my Fallout 3 setup, not my New Vegas setup. As you may have guessed, I'm posting it in here because there is very little activity in the Fallout 3 modding forum. The other reason is that I have recently had exactly the same issue with New Vegas. My best guess is that it's something to do with extensive load orders and bashed patches/merged patches. I used to think it related to either DarN's UI (something to do with a dodgy .xml file?) or EVE but now I'm not so certain.

Basically: Install mods (no particular culprit) > BOSS > Bashed Patch or Merged Patch > No mouse/keyboard input on the main menu.

It's happened so many times and yet I've never read/heard of a concrete reason as to what causes it. Does anyone have any ideas?