One camera that adequately fits all 4 criteria does not currently exist, as far as I understand and have experienced. However, you can get pretty close in 2 or 3 of those categories (especially if you leave off #4 ;-} ).
There's a thread on Photo.net about digis and what's popular in various price ranges. I got a little Olympus Stylus 1000 recently, which is pretty good for a party camera and video (secondary), but the best for video (stills secondary) is the Canon TX right now. You sacrifice a lot by making a camera do both, for reasons that basically have to do with the circuitry and sensors. What resolution video do you want? That will be a major difference between models. Very few stills will do video above 640x480x30-60 fps. I've seen stills from Sony and Canon video cams that were pretty decent, but only about 2 - 3 MP. I am guessing you'd want better than that for your stills (6 MP is plenty enough for 8x10, and more pixels is not always better in terms of quality versus lenses and circuitry).
Lately, I've been eyeballing the
Canon PowerShot S5 IS which has a nice tilt/swivel LCD and 12x zoom with Image Stabilization. Probably about as good as you'll get for under 5 bills. I might get one of these for Bonnaroo. The IS should give you a couple of stops (so you can shoot at 1/40 instead of 1/60), but at 12x you're going to get blur no matter what, unless it's bright light and you're over 1/125s.
"Good zoom" and "not blurry" are always at odds. The more you zoom, the more blur you get. It's very hard to get both unless you sink some coin into a low-F lens (1.2 - 1.4) and an SLR. Even still you'll see blur, but you can work with cameras that do at least 1600 ISO (most of them do now) and some level of EV compensation (+2 EV is most common, only the best can do +3 EV).
DP Review is my favorite camera review site, but for photography tips, Photo.Net is far more extensive. Here's the article on the S5:
http://www.dpreview.com/reviews/specs/C ... n_s5is.asp
The other thing is that if you're willing to spend 5 bills instead of 3, you're into the "semi-SLR" range so you get better lenses than the sub-compact types. There are dozens of cameras in this range. These will shoot one or two stops better (at least) than their sub-compact counterparts. I call these "semi-SLRs" but most call them "compacts". Panasonic and Olympus also make good models in this category. I'm sure there are others.
If you want prints, you're better off getting a good still that takes OK video. Video eats up lots of memory and it's harder to pass around to friends. A few minutes can easily eat up 100 MB, and that would be about the same as 1000 photos in a gallery at 1024x768 resolution. Though video is definitely fun on certain occasions. Other thing is most primarily-still cams won't do more than 1 to 2 min. of video (and that's asking a lot...the XT may be the only one that does 10 min....but it's more video than still, though the stills are comparable to the SD/Elph line).