Your day might get longer if you have to make electrical tests....which in this case you will. Either you can take a multi-meter and check continuity thru the water valve solenoid, or you can go to the icemaker itself and jumper V to L on the front to activate the water valve. If no water shows up in the icemaker, the valve is bad or the line is frozen up in the freezer.
If you are unfamiliar with electrical stuff, better call in a pro.
It's hard to say what melted back there by the compressor...there is a drain tube that drops down from the freezer which hangs in that general area. The tubing to the icemaker is a white 1/4" plastic line that runs from the water valve. You know, the place where the water lline connects from the wall.