Here are your parts
Replacement parts for FRIGIDAIRE FRT21TNCW6 Frg(v4) / Top Mount Refrigerator | AppliancePartsPros.com
the power is on, and you can hear it running, but nothing.
You have to determine what is running. You may be hearing the freezer fan.
Check if the compressor is running. You can usually hear it but should also be able to feel it vibrating and it should be warm.
Ive been told it might be a relay?
If the compressor is not running then yes it could be the start relay.
Here is a good link on how to check things
Appliance Repair Guide: How To Fix a Refrigerator - ACME HOW TO.com
And here is another one with more basic repair info.