It could very well be a ground problem. Check all your connections but I'm still leaning toward something in the main power wire. OK, this is going to get deep and sound weird, but bear with me. If you have no load on a power wire (nothing plugged in) you will read full voltage with a digital voltmeter even if there is only one strand of the wire still connected or a break in the wire that is just touching. This is because the digital meter has such high impedance and uses virtually no current to measure with. As soon as you plug something in though, the break in the wire or bad connection acts as a high resistance, and the point you're measuring at, downstream from the break, becomes a virtual ground. As there is no significant current flow past the break or connection, your circuit won't function and you'll read 0 volts. What I would like you to do, after checking the ground connections because that's easy, is stick a thin needle into the power wire at the solenoid, just past the fuseable link and measure the voltage on the needle both with something plugged in and not. If the voltage is the same, the wire is ok at that point. If you have someone that can help you, you can have them reading the meter at the fuse block while you wiggle the wire at the solenoid and see if the meter reading fluctuates as an alternative. Go to the 4 prong plug and measure both sides of it the same way. Measure just before the connection at the fuse block. When you find a place where the voltage changes, you'll know what area your break is in or connection is bad. We'll get there yet.
Steve