Car is dead... Just plain dead

Last night, I was drove my car home and it was fine, running great and all. This morning, I went out to my car and tried to use the remote to unlock it, and it didnt work. Gave up, unlocked it by hand, then went to start it, and nothing happened. No click or anything, no noise, absolutly nothing. Now the key won't come out and the ignition won't turn all the way back to the off position. I can't shift it out of park (which is gonna be hell when they tow it... dunno how they're gonna get it lined up). I'm thinking it's just a dead battery, since absolutly nothing electrical is working (i.e. the remote locks). Any ideas on what it might be?

I would try a battery before anything, but it could be the alternator as well becuase it seems like its not keeping the charge

I would try a battery before anything, but it could be the alternator as well becuase it seems like its not keeping the charge