Here is an easy way to virtually eliminate "thud" from the amp. All that is needed is 2 relays.
First relay would turn on when the car is on. It can be triggered via cigarette lighter wire.
First relay would short a positive 12V wire coming out from your PC system to connect the coil of the second relay. Other end of the could would be the PC's power supply ground. The second relay, then would connect the car's 12V (could be from the same cig lighter wire) to the amp.
Voila, you got yourself a delayed amp turn-on.