Hello Elfman.

I'm betting that your cabinet speaker amplifier chip has developed an internal short from Pin 5 (+12V) to pin 4 (output pin). This would explain why you see 12V on the output. There is a chance that the output is not shorted and the amp chip is railed to +12V due to another defect inside the chip. The amp chip is inexpensive ~$3 so just replace it if you are capable to doing the work.
I hope that helps.
Mark

You are correct in all your information.
The big clue is if the amplifier chip is so hot that you can't keep your finger on it. That does not mean 100% that the chip will get really hot.
It all depends on what failed inside and how it failed.
Hopefully you will be able to Ohm it out and see that it's different than the "good" amp readings.

Be careful when you use a solder sucker! We banned them at my company because it's too easy to damage a board.
Snip the pins like you said and remove them one by one. Usually a little solder braid will get the rest of the solder out of the hole but be careful that you don't rip the solder pads off the board.

Let me know how it goes.

Thanks,
Mark

Great!!
I did a similar repair last month to help someone out and the company he purchased the amp chip from actually sent him the wrong device.
It fit but it did not work. It threw us for a loop until I decided to just replace the chip again and then discovered what had happened.

Enjoy your game!
Mark