Some power rail is partially shorted. Probably a worn wire or a dendrite in a defective capacitor or a dendrite between two contacts on the board. I'd disassemble it, inspect all the wires, inspect the board for solder contamination (dendrites partially shorting between contacts, particularly at the power connector), and if you still don't find any problems, replace all the capacitors in the power supply, starting with any that look like they were made in China....
You might also try unplugging the FireWire cable before switching it on and see if the fuse blows when you plug the cable in instead of when you power it on. You might have a significant current leak between the DC output line and the ground in your FireWire cable.
If none of that helps, replace the fuse with a breaker. That way at least you don't have to keep replacing fuses.