freezer at 30°F, frig at 65 what is wrong?

We had a refrigerator like that many years back. It took me awhile to even discover. Milk would go bad, other things would spoil. I put thermometer's in the freezer and fridge part, but when I'd check the temps looked normal. We had just moved into a new development so I called the builder to check it out. He told me it was 'a run, no pump' compressor and said the compressor needed to be replaced. They came in to repair the unit, and called me at work and said "don't panic, when we were replacing the compressor somehow we knocked all the power out of the house, but we can get another compressor in about 2 days", they had been in several times before trying to repair that lemon, so I said no, there better be a new refrigerator there when I get home. They replaced the fridge.

It could be the compressor, but the newer fridges have these idiot warranties, so if you call for a repairman, you will wind up with 3 appts, one to come out and say 'son-of-gun, you're right, that ice maker isn't working' the second appointment comes when you call them back to say the part was delivered, they come out and attempt to replace whatever is supposed to be broken. If you're lucky, it will actually solve the problem, if you're not, step 1 and 2 will be repeated. At least that's how GE and Sears operate. The next time something breaks on my fridge, I'm calling an independant repairman.

A working refrigerator section should maintain a steady temp of around 38-45 deg F and freezer, should hold between 0 deg f and 10 deg F.
If something is causing temps to not go to 0-10 deg in freezer or to swing wildly..and there are not things blocking/covering the coils or fan or it's overloaded, the compressor or coolant being low could be the issue...but let me not jump ahead.

Here's a troubleshooting list to guide you to possibilities. Check for the following:

It's hard to say for sure. Compressor is a possibility but if it's gone or going say good bye. On an average, they tend to last 15-18 years or longer these days.

If you cleaned the coils and made sure all the gaskets are clean/not cracked and the doors accidentally aren't being left open, check to see if freezer is icing up at all?

If it were me, I'd look at the thermostat as it's easiest and cheapest to change.

If the thermostat (basically a rheostat. in English, it's analogous to a volume control) might be corroded or oxidized in spots, that wouldn't be unusual. That could cause the intermittent ok then not ok. Swap it out.

What have you to lose. You might be out $30-50 ..just as a guess.

{Edit: I just noticed in looking at you posting that this is 27-yr-old refrigerator. Give it a burial. It has served you well. If you replace the thermostat, the compressor will go soon enough. Undoubtedly it's running out of coolant through microscopic or larger pinholes that happen over the longevity of the unit.Why waste the $ ? Oh,and the new refrigerator you'd buy could save you an avg of $20-$30 per month on your utility bill due to the better efficiency.}

I just looked up your model on Kenmore website. This is a good OFFICIAL troubleshooting and parts list/costs list resource. Put aside my prior list of semi-educated guesses.
http://www.partselect.com/Models/3638784480/#Symptoms

There seems to be no compressor part available or listed on this site. For all practical purposes, I'm supposing it would not be feasible to replace.

Temperature control thermostat is no longer available

Defroster thermostat costs $12.50
Defrost timer $51
Freezer Door gasket is $75
Evaporator fan motor is $137
fan blade (for above) is $50
Defroster heater kit $138

Likely repair parts for specific trouble:
"Freezer section too warm" - Defrost timer ($51), 76% likely to fix
Condensor fan motor ( $172) 23% likely

"Fridge section too warm" - Defrost timer ($51), 74% likely to fix
Defrost Thermostat ($13) 10% of the time
Condensor fan motor ( $172) 8% likely
Fresh food door gasket ($75) 6% likely

No one should even consider fixing a refrigeration unit this old. It does not matter what is wrong, get a new one.

Yeah..I wrote that awhile back.

I put that troubleshooting info in case someone needs to satisfy some sort of peculiar repair itch.

A 27-yr-old fridge owes nobody anything. That is the equivalent of 2 lifetimes by today's standards.

Even when repaired, they'll suck up so much power so as to make it far more practical to just replace it.

this foodservice professional was attempting to agree with you.

And it will suck up way to much juice. When I was young and dumb I let a landlord stick me with a very old frig. It was a big chunk of my California Rates electric bill for a year. That is one that I would like back.

We would most likely want to see movies of the evaporator coil after its been successively a though so we can inform what the coolness model look similar.