I'd pay somebody to do it. The ways you could do it yourself are:
ethernet to the new compy
removeable media over USB (or a seperate USB HD)
buy a firewire upgrade card (if you can find one)
buy an external HD enclosure and take the HD out, connect it to the new computer, and grab your files
The last one will probably be just about as expensive as paying somebody, and that's probably what they'll do anyways. Besides, the iMac's ethernet and usb are both really slow, even when you're dealing with as few as 4 GB