Here your parts
Replacement parts for WHIRLPOOL GU1200XTLQ3 | AppliancePartsPros.com

Here is the tech sheet
http://www.servicematters.com/d...0Sheet%20-%208537797.pdf

I would check the heater and hi-limit thermostat but I would have thought that you would have also noticed long cycle times since it did not heat up the water.

I would also check the vent wax motor if your unit has one, could be it is not opening. If you open the unit during a dry cycle and it is very hot but still the dishes end up being wet, then this would be at the top of my list.

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.