If you can, look at the PC board, usually this indicates a blown amplifier chip, transistor or FET. The poping sounds can be the transistor base feedback, because of the RC filtering and amplification. You can sometimes see brown, or lifted clad on the board, if not always lick your finger and touch the top of an amp chip. I say lick your finger because if it is shorted, it is going to be hot!!!!! When you lick you finger, you will hear the sizzle before you burn your finger, just be careful not to touch the high voltage.

First off nothing should pop when turned off next it could be a grounding problem external or internal or worse an audio output problem take a volt meeter and turn key to on check the ground and positive on the amp should read 12 to 14 volts do same with ground and remote wire if these both read correct remove the back set your meeter to the diode setting the audio outputs are usually the larger ones but sometimes not take your leads and touch out side legs then to the outside to center try each one every way you can switching leads if at any time the buzzer stays on or goes to flat 0 then that output is bad if all check good i would go through the car making better connections and cleaning up any wires that might seem to be faulty maybe even replace your RCA cables
im running 18 speakers and 8 amplifiers in my car and i have done this several times :( but i don't pop unless something is wrong hope this helps