This should be possible as the AV port on the TRV480 can accept input signals. You should be able to connect an other analog source to the TRV480's AV input and pass the signal to a computer thru the TRV480's DV (firewire) port.
you usually need to subscribe to a digital service such as cable, or direct tv. digital tv is the type of broadcasting the signal. most digital tv's will work without a digital reciever, since it's built in, but general free broadscast stations, nbc,...
Please post the manufacturer and model of your camcorder and computer. Doing so will drastically reduce the hours of writing it would take to cover all possible permutations of equipment and solutions. You have to know what the video output(s) of you...