Sure. I'm not sure about $1,000, but there are several top line digital SLR's that will perform at a burst or continuous rate of 5 fps or greater. The problem is, they can not do this for an indefinite period of time. You will be limited by the buffer capacity vs. write speed equation. Without discussing the cameras that sell for $3,000 or more, I know of some that will deliver for you.
Canon 30D - 5 fps (max speed)
Canon 40D - 6.5 fps (max speed)
Nikon D200 - 5 fps (max speed)
Nikon D300 - 6 fps (max speed)
Sony A700 - 5 fps (max speed)
I own the D200 and D300, which are 10 MP and 12 MP cameras. If you capture in a reduced size, you can almost keep going until the card is full. A 6 MP file on a D200 is usually about 3-4 MB, so a 2 GB card would hold over 600 shots. Worst case would be that you have to shoot maybe 100 frames and wait a few seconds before continuing. CF cards are avilable up to 16 GB and beyond, too, so find a size and do the math. A D200 is available for abuot $1,300 now, plus a lens and card. I don't know what your demands are for a lens, but you could get almost ANY Nikon lens and it would be better than most video lenses, so lets say you can get a lens for $200 or less. The D300 sells for $1,800, plus lens and card. For your purposes, the D200 would be exceptional.
Go here and click on "In-depth review" for each camera and then go down to the page about "Timings and Sizes" and you will see performance data for continuous capture rate on various cards. The tests seem to be generally only for the largest file with the best resolution. One example: http://www.dpreview.com/reviews/nikond200/page12.asp
This brings up another point. You do want the fastest write speed for a memory card available. One industry leader is the Sandisk Extreme III, which is called a 133X card. 133X or higher is what you want for the ability to shoot as many continuous frames as possible.
I see that the Nikon D300 will capture 100 full sized, high resolution images at 6.1 fps onto a Sandisk Extreme IV card. You could select slower frame rates, which will affect the buffer load/transfer rate also. In your case, this would be an advantage if you want extended continuous shooting.
There aer many variables that I am not familiar with, but I have seen it in black and white that the D300 will capture 100 full size, high resolution images into the BUFFER before it shuts down. It is my SPECULATION that you will get more into the buffer with a slightly slower frame rate and somewhat smaller file size, but 100 might be a hard and fast limit. If the buffer fills, the fps rate will slow down to match the buffer-to-card transfer rate. You could do 100 frames and pause a few seconds for the buffer to unload if you want to maintain at least 5 fps.
Another thing that occurs to me, though, is that there is a limit to the number of shutter actuations that you can use before the camera fails. The D200 shutter is rated at 150,000 shutter actuations and the D300 shutter is rated at 200,000 shutter actuations. If you shot at 5 fps up to the 100 frame buffer limit, this would take 20 seconds. Allow another 20 seconds for the buffer to unload completely, just for the sake of argument. Shoot again. You could go through this cycle only 2,000 times before you risk trashing the camera. That would take less than 24 hours. You can have the shutter replaced, but obviously that is not inexpensive. If you will be exceeding these limits, just check into replacement costs before you buy. It's still cheaper to buy a few and toss them than it is to buy one $50,000 industrial camera, though.
http://www.dpreview.com/reviews/compare_post.asp?method=sidebyside&cameras=canon_eos30d%2Ccanon_eos40d%2Cnikon_d200%2Cnikon_d300%2Csony_dslra700&show=all
I do not know about direct capture on a computer, but perhaps someone with that expertise will come along.