Resolution (well.... a work-around):

I'm a student, use Maya in class, needed at home, got the trial.. blah blah.

I Had The Same Issue! Couldn't select polygons, (Could but only in the out liner).
Had some more issues, manipulators weren't showing up right, rotate didn't work and some other fun stuff

To make a long story short after tons of trial and error it ended up being that maya was having a compatibility problem with Windows 7.

I solved it by getting virtual box from oracle (free) installing XP in it and then re-installing maya inside an xp VM.

BINGO! that did the trick, so it was windows 7 and I think an issue with my video card, all i know is its working in XP.

And sorry helpful posters from earlier, it's not preferences, pref file or env file or deleting the maya folder or anything inside. It's an open GL issue with win 7/video card & maya

XP to the rescue.

Maya is still the greatest 3d prog of all time and anything you can do in other prigs you can do in maya, you just have to try a little harder to figure it out lol.