I agree with scifijedi. You shouldn't consider anything other than 3CCD's, and you can definitely get a used one for WELL under $2G.
HOWEVER...
Lately, I'm becoming convinced that DSLR's are eventually going to make "regular" video cameras obsolete. They shoot at 24FPS, and are capable of a much shallower depth of field, and therefore have a more film-like look. I have a friend who's been shooting on them, and the results are gorgeous. It's sort of a new trend, so there are some inconveniences, but Canon has recognized the potential new market for DSLR's, and they're developing new ways to make this method beneficial to filmmakers.
The Rebel t2i is $800, and you'll be shooting in HD! You might also want to check out the Canon 5D or 7D. Then, you can use all that money you've saved to buy a couple nice lenses, a cheap (but decent) mic, a boom pole, and a portable digital audio recorder (DSLR's can't capture external sound).