The lights are working, but the compressor won't turn on.

Does the fans come on . If so than you may have a bad start relay or compressor

Sounds like your control switch is going bad. Good thing you have the quick freeze button. You may want to go ahead and replace it. The whole thing will go out soon. This is something you can replace yourself.

if it just hums or buzzez you will need to check the start capacitor on the compressor if it is stuffed you need to buy around 15uf---25uf cap @400volts depending on the size of the motor

GIVE IT TIME SO THE THE SYSTEM COULD STABILIZE IT SYSTEM FOR A FRESH STARTUP. OR HAVE CHECK TO ITS OVERLOAD UNIT THE COMPRESSOR MOTOR.

Turn it round and check the electrics for the compressor are dry. You probably flooded them when defrosting and may have shorted something. If it still won't start with everything dried out, call a fridge technician

Well a freezer is easy to repair. The circuit goes from one side of the power cord to the cold control and down to the compressor then out to the other side of the power cord. Id the control or compressor relay is open then she won't freeze. All the parts to it are listed HERE.
From the list I see an overload for the compressor. If that one is open it won't freeze. Bypass the temp control wires to see if she runs.

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Possible that the gas pressure is down to low gas or leak on the system. Also it can be due to faulty thermostat, faulty compressor if the compressor is working all the time and reaching the set temperature. Also if the compressor is not cutting off this must be a suspect.

I use this on a regular basis and have had no issues. I believe it will work. If I had some numbers from the compressor plus a brand name such as Copeland, Tecumsah, embraco, etc., I may be able to tell you more about the compressor HP.

1) Check the compressor working or not.. Air cooling type condenser fan may be not working properly.
2) Compressor working but not properly. Last side of condenser (Filter) Light Heat or not.
3) Inside Cooling area do not get cooling. may be gas leakage problem.
4) My opinion check Gas pressure Low and high side.

What makes a compressor to run constant is the thermostat. Bang on it to see if it will turn off. turn the setting to 1. if it still wont shut off replace cold control (aka thermostat)
worry about the light later hope this was helpful