I love this stuff, and this silly problem is standing between me and my first FPV flight. ARgh!!DF#@$#
If your APM lights up OK when running only on your batteries (not the USB) then it's probably OK. There's a fuse between the PM input and the main power rail of the APM. If you blew that the APM won't power up via battery. But it could still appear to work when plugged in to the USB because that connection bypasses the fuse.
If you hook up your APM to both battery and USB, have a look at the HUD in Mission Planner. If it's reporting correctly and it's showing your right battery voltage then your APM may be OK.
Your PM may have blown out before damage occurred to your APM. But there's no buffer for the ESCs. They got the full brunt of reverse polarity and may all be blown. Times 6.
An easy check would be to connect one or two directly to the output of your RC receiver and see if you get any response. If not, then you have bad ESCs. If you do get a response from the ESCs, then you have a damaged APM.
I did something of even greater dumbness by hooking an APM setup to an 8S power source. It wasn't pretty. It took out the PM, the APM and MinimOSD. The GPS survived. Surprisingly my Castle ESC lived through it (it was a fixed wing setup so just one ESC)
After replacing the PM my APM is booting up happily from the battery
Yep... I tried the direct receiver -> ESC test and no response. I'm pretty sure I fried all of my ESCs x6. :)
Now I'm off to shop for new ESCs. The castle ones look nice. Not sure if I'll go with those or direct replacements from the 3DR store.
Thanks again for the debugging steps, really helped a lot!