Well, the sub seems to light up and seems to recognise a signal. So I think you can rule out the power supply and input stage. That leaves either the output stage (transistor and capacitor asthe main suspects) or the driver itself being borked.
A quick test on the driver is to disconnect the cables to the terminals, then rig up a AA battery with a couple of fly leads. All you need do is touch the leads momentarily on the speaker terminals. You should hear a clicky-rustly sound as the driver moves. If it doesn't move then it probably indicates that there's a problem with the voice coil. Either it has distorted due to excess heat and jammed in the gap, or it has shorted. But I'd expect a short to happen during a peak in the music rather than after the sub is switched off.
The other area is the amp electrics. Faulty capacitors show up as bulging either at the top or sometimes at the base. You can Google for what to look for. This has been quite a big problem in the electronics industry so there's a lot of sites with good images of the issue. A quick test for an intermittent capacitor is to put some heat on it. A hair drier will do, or a hot air gun with caution. When warm they can be coaxed back in to life briefly. This is a test you can do with the capacitor on the board, so it's useful for quick fault-finding. The next stage is to remove the cap (be careful of the terminals, they can give you a belt) and test with a multi-meter that includes the F farad scale.
Transistors respond to cold. So if there's no obvious sign such as it being blown to bits or a dirty great scorch mark then a can of freeze spray can give individual components an icy blast.