that will do what you're talking about. Here's one:
http://www.zzounds.com/item--MDOPROJECTIOIt's a bit outside your preferred price range, but I think it works in the way you describe. The mixer plugs into your computer via a firewire cable (so you might need to get a firewire card, but I think they're pretty cheap).
If I've got this right, the mixer captures your audio as it's recorded, but it doesn't store it - it just transfers it directly to your computer's hard drive via the firewire cable.
This means you don't need a fancy sound card, because there's no audio going into the computer, just the data files that the mixer is producing as it records your sounds.
As you record, those data files are transferred in real time into any standard audio editing software on your computer, Pro Tools or whatever, where you can immediately start manipulating them.
I believe you can mix using the software or the mixer or a combination of both - it's got motorized faders so I think you can manipulate them from the software and vice versa.
It's got eight inputs although I don't know if you can record on all eight simultaneously. You probably can. At the very least, you should be able to record on four at the same time.