U-line origins 75R fridge not cooling

this was given to me, i don't know anything of its history...
when i plug it in, the fan and compressor come on as if it wants to cool. it never gets cold, just keeps running. i can hear fluid moving through the system, so i know it's not empty. when i turn the temp control to the warmest setting, the compressor turns off, and the fan stays on.
we just had our first child, and i'd really like to have this mini-fridge upstairs for kid milk in the middle of the night. we only have one local appliance repair place, and they want a ton of cash just to diagnose the problem. can't afford to dump a bunch of money into this. i'm a handy kinda guy, if i knew what to fix, i could do it myself (if it's fixable). is there a way to home-diagnose maybe the thermostat or any other part that may be the issue? the lowest price i've seen on a thermostat is about $55, and i'm not going to just buy parts and hope that's the solution...
thanks much,
mike