The single biggest problem I saw with car installs was the ground on the power amp becoming intermittent, especially if grounded to the frame or body.
When it goes open the new path for the ground current becomes the RCA cables. This causes the head unit to vaporize a trace and then things get weird (and can do what yours seems to be doing).
Do you have a transformer-type ground loop isolator? It should go on the input of your crossover, which is usually in your trunk. A crossover or EQ could be similarly damaged too. Cheap isolators roll off the low end, buy a good one, I recommend the Edcor models.