Unit was purchased new 20+ years ago, installed once and never moved. There is an automatic ice maker, but there is no water line hooked up to the unit, so the ice maker arm has been in the "off" position the entire time. Everything has worked fine until a couple days ago.

It became apparent today that the fridge and freezer are both failing to keep cold at their previous temps. It's still plugged in and I can hear it whine faintly like something is trying to turn on, and then it stops whining. After a short time, the faint whining starts again and then stops. When I open the freezer section, I can hear a very faint sound like a timer. Water is on the floor near the front left corner of the appliance, I assume that's from defrosting due to not staying cold, since it's not a whole lot of water.

I think the culprit might be the condenser motor, from looking up info here on APP, but would like some expert opinion about which part(s) I need to buy and replace, so I can be more sure.
Thank you!

OK, I have checked the back machine compartment, and the condenser fan spins freely, though it's pretty dirty from the years. Also the compressor is hot. That's after being plugged in up until about 30 minutes ago. I believe that indicates the compressor and starter are functioning.

One thing I'm unsure of is how to get the back panel completely off to continue troubleshooting (and eventually repairing). I've removed all the screws, but the water valve assembly seems to be holding the panel on still. I don't want to start disassembling anything more than I have to...

Continuing to work on this. I carefully disassembled the parts that were blocking me from getting the whole back cover off so now have access to see everything clearly. I watched a video on how to check the compressor (using multi meter, checking continuity between the 3 prongs, also checking for a short)so I followed instructions and all the checks between the prongs gave me a tone, and the check for shorts gave me no tone on any of the prongs. The start relay doesn't rattle noticeably when I shake it. I can't feel any air flowing inside the freezer or refrigerator compartments. But it's not like the freezer is cold while the refrigerator isn't, neither is cold at all.
The compressor for this model is out of stock here on APP. I'd really like to be able to get a solid diagnosis of the problem so I can know whether to call someone for help or if I can still do this myself. (I know my screen name is "newbie", but I've been DIY'ing my appliance problems for some time now.)