I was gone for six hours and when I returned, there was water on the floor and in the fridge/freezer. I can hear it running, but it is no longer cooling. I unplugged it for the night and it is still not cooling the next day. Does this model have a common problem?

SOURCE: amana refrigerator

Sounds like it has either a bad compressor relay or if the brand name of the compressor is Tecumseh, it will need to be retrofit to a more reliable longer lasting Embraco compressor.

SOURCE: DEFROSTING/ WATER RUNNING ONTO FLOOR & INSIDE FRIDGE

Check to see if the run-off tube at the back is plugged.

I dont know how old the fridge is - but if it a couple years old check at the back or the fridge - there should be a tube running down the back of the fridge down into the bottom tray. This tube funnels water from the freezer (condensation, or water from the defrost) down onto the tray holding the compressor where it evaporates with help from the heat off the compressor. Sometimes this tube can get plugged up with some scum or mineral deposits, causing the built up water to drain from inside the fridge.

The tube shouldn't be too hard to remove and clean out with some hot water and pipe cleaners. Had the same issue on on a GE fridge last year.
Hope this helps!

SOURCE: Whirlpool Fridge Freezer not working fridge is

ID THERE FROST BUILDING UP IN THE FREEZER?IKE

SOURCE: fridge is no longer cooling. ER where the

Sounds like the FF(Freezer Fan) is wearing out or is worn out. This assembly supplies the circulation for the freezer as well as the refrigerator. When is slows down or stops the circulation of cold air to the refrigerator is the first thing that is effected. The minimum cost to replace this assembly is around $300.00

SOURCE: Stopped cooling but i can hear running

The overload/relay is probably bad .This is the part plugged onto the compressor , with 2 or 3 wires plugged onto it . You can easily replace this part . Be sure to have your model number when ordering .