This is hilarious. Even while trying to convince somebody to NOT buy DSLR, I've convinced them to buy DSLR. I should start demanding commission from Canon.
Okay, first, the reasons you might not want DSLR:
You can't just press "record" and let it record forever. This would make it difficult to shoot documentaries and/or special events like weddings. Every shot you get is saved as a file on your SD disk, and there is a maximum file-size.
Also, those SD disks can be kind of costly. If your camera is constantly on record, for many hours, you're going to need a whole lot of disks, so again, this would be a horrible camera to shoot weddings.
And, do you really wanna have to change a disk every time you run out of space? Changing a disk is no big deal for a narrative shoot; it takes a few seconds. But on a documentary shoot, those few seconds you just lost could prove to be seriously detrimental.
Also, DSLRs can overheat. As you've pointed out, they're designed, first and foremost, for still-photography. The video capture puts a lot of demand on the innards of these cameras (and their batteries), and they will, from time to time, just tell you to stop. No big deal on the set of a narrative. VERY big deal for a documentary or wedding, etc.
For the intents and purposes of video, DSLRs do not have auto-focus. On a narrative shoot, you're an absolute idiot if you want to use auto-focus (with maybe a few extreme exceptions). But for a documentary, or an improptu skating shoot, I think it's perfectly acceptable, and perhaps often advantageous, depending on the situation, to want to use auto-focus.
These cameras are sensitive. Any jostling, while shooting, will cause the image to wobble. Then, there is the "jello" effect. If you have a rapid pan, vertical lines will become bendy. Look at the buildings in this clip:
https://www.youtube.com/watch?v=nhfQnIQPMjM
Finally, the audio is shitty. After having done the research, I wouldn't even consider plugging an external mic into any of these cameras, even if you're using an XLR converter. On a narrative shoot, that's no problem; in fact, I really prefer having a seperate audio recorder. On a documentary, you probably won't have the luxury of a boom-op/audio-recorder.
Reasons why you might want to buy DSLR:
I believe M1chae1 said it best, in a seperate forum, when he pointed out that they give you the best bang for your buck. In this price-range, there is simply no comparison in image-quality. You would have to spend SO MUCH more to get an image as crisp as what can be attained with a DSLR.
Also, you finally get to play with depth of field. All cameras have depth of field. But if shallow depth of field is what you want, DSLR is your friend. HDV-users are devising all sorts of complicated conversion kits, and their results still aren't as good. DSLR users just drop that f-stop, and boom!, you've seperated your foreground from your background.
They shoot really well in low light. The following clip was shot inside a house, with NO LIGHTS. We just opened the blinds:
https://www.youtube.com/watch?v=spUtEn1Wajg
No HDV would be able to get the same quality image, under those conditions, and this isn't even an extreme example.
And then there's the ability to change lenses. That's a huge plus (but also a huge expense - good glass ain't cheap).
All that said, I don't think you should make your decision so quickly. No disrespect intended of course, but I can tell, based on the questions you're asking, that you are a complete rookie. Even if you go with the super-inexpensive DSLR, it's still a considerable investment. Don't just take my advice. Do a bunch of research. Whatever camera you choose is going to be with you a while.
Oh, and to finally answer your question, in your price-range, you only have two options -- Canon 7D, or Canon T2i. The 7D does have a number of advantages over the T2i, but in my opinion, they are negligible, and I just shot a feature using both the T2i and 7D. At the end of the day, the footage is pretty much the same, between either of those cameras. If you have a budget of $2000, I would think it best spent to get the less-expensive T2i ($800), and use the rest of your money to get audio gear and a couple lenses.
But that's IF you decide to go with DSLR. I'm happy to be on this bandwagon, but that doesn't necessarily mean it's the best thing for you.
Why are SLR cameras so good all of a sudden? I mean do they have a good on board microphone?