Re: Sub/Amplifier Problem
Although I'm far from an expert, I have some experience powering car audio gear with a power supply, and was surprised how much output I got from FAR less than rated power (as measured by a DC clamp meter). Presuming your power supply puts out rated power, my personal experience suggests there should be considerable output - certainly more than "some sound" (which I interpret to mean barely any output at all).
Without a cogent theory to explain it (why there's no sound at all in the car, and why low/choppy output on the power supply) I'm guessing the amp is having issues. Maybe there's another completely unrelated issue in the car hook-up? Seems to me, judging by the power supply instance alone, that the amp is having issues.
I'd try running the subs on a known working amp, to see if they're the problem. Check them with an ohm meter first, to see if there are any issues. I'd also try running different sub(s) or speaker(s) on the amp and power supply arrangement, to see if it does the same thing.
That's just my $0.02. I'm sure others more knowledgeable than me will chime-in.
Re: Sub/Amplifier Problem
I was going to ask about the remote wire, but it looks like that's jumper'ed and always on.
I'm not sure if you need the jumper between the channels when you bridge them, but that seems unlikely to be the cause because it's the same on-bench and in-car.
You seem to be following all the right steps. I'm not sure about this one!