The firewire connection on the JVC camera is the DV, not the S-video.
You are in luck with your laptop. It has a firewire connector on the right side, called the IEEE 1394 connection in the online manual which I found here: http://support.dell.com/support/edocs/systems/ins1521/en/om_en/pdf/RT722A02MR.pdf
That means you just need the cable to connect the two machines. I'd take them both down to Best Buy or Frys or whichever electronics store you prefer and find a firewire cable that will fit them. I would tell you to get one at monoprice.com for cheap, but firewire cables can have 9, 6 or 4 pins, and I'm not sure which you have. The accessories listed at the JVC site have both a 4 pin to 4 pin cable and a 4 pin to 6 pin cable. Just looking at the pictures, I'd say you need a 4 pin to 4 pin cable, but I'd hate to lead you astray trying to advise you from long distance.