I would also recommend the Canon XHA1 - I bought one about 6 months ago for just under $3000 - you might be able to find one used for the 2,800 - 2,500 , though I wouldn't count on it, as they seemed to be pretty popular items on ebay.
The quality is excellent, and it is small enough to go with me on long hikes or even backpacks. I bought it, as the cameras that take HD video are fairly limited when it comes to audio recording, and I'm currently working on a feature length documentary - so audio is just as important as video. Also, the SLRs that shoot video aren't very useable in terms of pan and tilt.
I know the camera might cost $3000, but when you're budgeting for it, you'll need quite a bit more - as there are some other things I would recommend. If you buy a video camera, you'll need a good pan / Tilt head - fluid ones can cost well into the thousands, but bogen makes some acceptable options for a couple hundred. Also, you'll want to get a good shotgun microphone - this is useful for people, background sounds, or wildlife to name a few - they typically run 200 - $300 for a decent model - of course you could always spend more.
If you're planning to record people, then that's another story - you'll also need a lavalier microphone - probably 200 - $300 or so. You'll also want to pick up continuous lights if you don't have - especially if you'll be recording indoors. Tungsten lights are the most cost-effective, and can be purchased on ebay for a couple hundred dollars each. HMIs are nice, but are very pricey - well out of my range in the thousands - used. You also want some good light stands / C-stands to hold the lights, diffusers, reflectors and such.
As you can see, there's a more expense than meets the eye here. The Canon also offers a Direct-To-Edit DTE solution for the camera - this is basically a Hard Drive that you plug into the camera - it can record to this instead of to a tape - these can be handy and cost effective, though storing your video files on your hard drives will take up a lot of space - about 200 MBs / minute in RAW - close to 1 GB per minute transcoded into ProRess 422 (apple's newest editing codec).
All to say, video is a lot of fun, but don't expect the only cost involved here to be the camera - the batteries are several hundred dollars for the Canon, and I would at least get 1 backup of the larger capacity battery.