Jabsco "Quiet Flush" right? Heehee... We have 2. I love the fact that they never clog. Simple heads. But.
Before you replace the solenoid:
1) Put your hand on it to see if you can feel it activate when you (or someone) hits the button. If you can't feel anything, put a multimeter on it, verify it's not getting
power when you hit the button (plus to the solenoid, minus to a common ground). If it's getting
power, then your problem is the solenoid. Disassemble it, CAREFULLY, it's easy to lose that small spring. Clean it well, it's probably got a grain or 2 of sand in it. That's usually all it takes. If you need a new solenoid, PM me, I have a source for these (other than Jabsco) somewhere...
2) If it's not getting power, it's the switch. Ugh. Been fighting Jabsco on these crappy switches. They use an underrated switch. It gets carbon on the contacts. New switches are +/- $130. But, if it's a newer switch (not the red button switch) you can pull the Carling part number off the side. You can also clean the contacts with contact cleaner. Be careful, the contacts are silver plated and it's easy to take the silver off with too much aggression.
3) EDIT: One more thing. You say it fills fine when you open the faucet? It's probably a weak or obstructed solenoid. We had this happen. You take pressure off of it and it opens. Just replaced it.
I'm trying to get info from Blue Seas about a better solution. Jabsco says they are working on another redesign of the switch.
Good luck.