I have had nearly the same problem with my Panasonic PV-GS31. It worked fine with my old PC, with Windows XP sp2. I just plugged it into the USB port, and was able to download from the camera to Windows Movie Maker. But, it was only a Pentium II 400mhz, and I just upgraded with a new Dell w/ AMD 64 duo, which came with MS Vista.
Now, however, the new computer won't recognize my camera, even though I get a 'ding' when I plug it in. The Vista version of Movie Maker says it couldn't find any DV camera.
I next downloaded the USB drivers from Panasonic's website:
Panasonic Product Support - Camcorder Downloads
and after installing them (which turned out also to be a pain in Vista), my camcorder was still not recognized.
I don't have a firewire card for this new computer, and from what you say, that probably wouldn't help anyway.
I've emailed Panasonic's customer support, but no response yet. I'll have to find the time to call them, but I doubt they have a solution. But, if you learn how to correct this, please share it.
thanks