Check the voltages, on the motherboard, by referencing the manual.
You'll have to become adept at reading the manual and diagram nomenclature, and tracing pins on the mother board. Checking voltages on the fuse section would be an easy way to verify voltages, too.
Or, reseat the cards in the top section. Sometimes a loose card can cause a voltage to drop out.
That's the only thing I can think of, based on your description. It still sounds like a voltage problem, based on what I've seen previously. I'm making a few assumptions, of course.
You could always test the voltage across the two leads on the solenoid, itself. It should have two states, zero (open solenoid), and charged (closed solenoid). The voltage should hold steady, when energized. If it pops to a voltage, momentarily, and immediately drops out, it still sounds like a fuse, voltage or power supply issue.
I hate to beg the question, but you replaced the fuses. Were any of the original fuses actually tested? It seems like an obvious dumbass question, but I had to ask. An actual test of the fuses would at least tell you the state of the fuses, themselves, and the effectiveness of your troubleshooting and repair, so far. There's nothing say that if a fuse blew, that it could not blow again, but unless you test the fuses, it may be hard to tell. Some fuses are opaque, and some are glass, so testing by visual inspection is only half effective as you think it would be.
There's always the option of seeking a service technician to do the job, if DIY isn't getting you anywhere.
