Yes, the valve handles in the box follow standard procedure and need to be in line with their hoses to be "on", and perpendicular (90 degrees) to them to be "off".  A quarter turn is all that is needed.

If you open the outside access door behind the refrigerator, Keith, you may be able to locate the icemaker's on/off solenoid.  If it's like mine, it will have a 1/4" line going in one side of it, and one coming out.  When the icemaker cycles and calls for water to fill the tray, a switch activates the solenoid's valve, allowing water to flow into the icemaker itself.  

You could pull off the hose from the "in" side of the solenoid with your fingers, aim it to the ground, have the Mrs. turn on the water pump, and see if water flows out.  If it does, you're okay from the water pump up to that point.  Turn off the pump.  Replace that hose.  If you have the refer/icemaker manual that shows you how to force an ice cycle, follow the instructions (with persistance, you may be able to find those instructions on the refer manufacturer's website online).  Remove the line on the solenoid's "out" side, aim it to the ground, turn on the pump again, and force an ice cycle to turn on the solenoid.  If water flows, then the solenoid valve is okay, and you should get water in the ice maker when the outlet hose is reattached.  But if the solenoid valve isn't getting an electric signal from the icemaker, then something is haywire electrically.  

Keep in mind, the icemaker side of the refrigerator requires AC to run, not 12v. DC.  And our refer won't run off the inverter either - it draws too much juice;  you're either on gas, generator, or plugged in.  The icemaker won't work if you are just on gas - it needs 110v AC.  And it has a seperate cord that needs plugging into an outlet in addition to the refer's cord;  check that both are in their outlets behind the outside refer access door.  

Also, the solenoid may have heat tape around it to help prevent wintertime freezing of the valve;  if that ever failed, your solenoid may be damaged from freezing and need replacing.  I usually take extra steps to drain and blow out the solenoid and attendant lines when winterizing, just in case.  But some pump RV antifreeze into the icemaker instead.

Hope there is something in all this that helps.

-Joel

Hmm
pump is on
freezer is cold (on for 24 hrs so far)
valve is twisted all the way out AND the T handle is lined up with the hose.
water tank is full
and yet, no water coming into the ice maker.

Just checked in the outside compartment and found the line from the solenoid to the ice maker busted.  The plastic is brittle, so must get pretty hot in there.  There must also be an electrical disconnect somewhere, as the solenoid is not calling for water.  I'll look for that, after I repair the water line.

One obvious thing that wasn't mentioned, Keith, as sometimes the solutions are simpler than we think:  is the bail on the icemaker up or down?  Like most icemakers, residential or RV, the bail has to be down for the unit to make ice.

-Joel

You can blow out the line, by putting air on the water system.    
All you have to do is make a jumper to open the water solinoid.
Take a extenion cord and cut off the female end.  Put female lugs on the end.
Unplug the solinoid wires, and plug the cord you made onto the solinoid.   Plug that into a 110 volt outlet and the water line will be open for air to purge the watermake line.
Great way to put antifreeze in the icemaker, when you winterize.