Sounds like it's dead - which is actually very good news, as the alternative was the mechanical end of the valve inside the tank assembly. Thanks for your help. I feel better about just going out and buying a replacement part.
If you can get at the actual coil you could probably wind another one too, just take the old wire off and estimate (easy) or count (boring) the number of turns on the coil, then just go to an alternator shop and buy a spool of the same sized wire, they usually have a variety of sizes of magnet wire. If it is a tiny coil then radio shack sells small amounts of magnet wire that might be enough to wind another coil.
The easiest way to wind a coil is to mount your base on a drill and use the drill at slow speed to spin the wire on to the coil, kind of like putting thread on a bobbin on a sewing machine, but anything that spins, an old record player, or whatever, will work. Actually you might be able to spin it on to a plastic bobbin on a sewing machine if the coil is small enough.
Another thing that works for small coils is to wind the coil around a drinking straw and use a nail as the core, the nail slides inside the straw when you apply power to the coil.
None of that works if the solenoid coil is sealed inside of a plastic enclosure that you will have to destroy to get at it, however, unless you feel like just building another one, or encasing it in resin or something.
If you get too many turns on the solenoid it'll make it have a stronger force, too few it won't be strong enough, so you want to try to get about as many turns of the same sized wire as you can.
If you bought the coil wire in a big spool you'll have some around for next time ...