Every time my deck powers up or powers off (when starting or shutting off the car) the sub makes a loud "bump". I have a late model JVC deck and a 300 watt internally powered 10" tube. The sub has a separate fused line off the battery.

 

That happens sometimes, usually with a cheap amp. If the amp doesn't mute the input when it powers up, it can cause the power spike sent from the deck to get to the subs. Unless it's excessively loud, it really isn't causing any damage.

 

your problem is most likely from a bad ground. make sure your ground from the amp to the chasy is getting a good connection. try to make sure its not just on top of paint, it should be bare metal.

 

I don't think a ground will effect turn-on thump. Turn-on thump is caused by voltage spikes from the source unit, which don't really have anything to do with the ground.

 

I had a rockford 500 that did that...i returned it and they said it was due to overheating

 

cheap amps do this, there are products that'll fix it
http://www.davidnavone.com/amp.html

 

I had the problem with my rockford amp and subs, It was just a bad ground, fixed in in about 1 minute.