If a camcorder isn't detected in any computer it's connected to, the camcorder may have a non functioning firewire port.
If some computers can detect it but not others, it's either Windows playing silly beggars (see above post about device manager), or an iffy firewire card (or port) in the computer.
One of my JVC camcorders has a blown firewire port due to it being connected to a computer with the 6 pin end (computer end) of the lead being plugged in the wrong way round. Oops