Strange electrical problem

[Crazy_pilot]

My car decided to start acting up today.

I'll describe the symptoms as best I can, they're odd.

First, waiting at a red light the radio (stock) started to make random thumps from the speakers, still playing tunes. Light goes green, I pull ahead to the next light. The thumping gets worse, so I turn the radio down. The speakers start putting out a short electic noise and the occasional thump, then the radio shuts itself off.

Next the real trouble starts. The light goes green, but when I push the pedal the engine nearly dies. It repeatedly gave short bursts to ~1200 RPM, then stopped firing, but restarted before the engine had stopped turning. It did this over and over, taking maybe 1-2 seconds each time. I managed to get it pulled over and parked.

The car kept running, and after about a minute of this the engine began running normally again. Revving normally, idling normally...I turned it off and started again, all normal.

I get the rest of the way home, but as I'm pulling into the driveway the speakers start thumping again. In the driveway I roll the windows up and close the sunroof, and they're barely moving. Revving the engine to 2-3K RPM has no effect on the window/roof speed. Also, the air bag and ABS light started to light dimly.

I just checked the battery, it reads 12V bang on.

So I'm at a loss as to what this could be. Any ideas?