High Temp light will not go off even though the freezer seems to be working. Compressor does not stop running

There shouldn't be any 'jingly tone' at the end of every compressor cycle. You could be hearing something else making a sound after the compressor stops.

From what I read, the "L." that you see on the control panel indicated that the controls have been locked. According to the manual if you hold down the "alarm reset" button for 3 seconds the "L." will disappear allowing you to control the temperature again. I don't as of yet know what is causing your overall problem though...

it could be that your fridge,freezer setting is not turned up high enough to keep the freezer cold enough.turn it up to setting number 5 at least and if that dont do it u could have a faulty thermostat.have it checked by a engineer.

The compressor has lost its start capacitor. This is not hard to repair. http://www.appliancepartspros.com/frigidaire-compressor-run-capacitor-5304464438-ap4315853.html

In case the freezer not getting cold. maybe the tube is leaking .the freon gas scape. or your compessor is defective

red light flashing means temp. is too high (not freezing) just an indicator to let you know that there is a problem
let me know: the freezer temp. (use a temp. reader)
any unusal ice build up on the back freezer panel?
is the freezer fan running?
compressor running?
parital frozen foods?

need to know so i can help you

the loud buzzing is the freezer high temp alarm. dont know why its warm though.
make sure you don't store anything on top of or on the sides of the unit as the condenser of most freezers are buried in the walls of the unit and it will over heat the compressor. if unit is in a hot garage this will compound the problem.

Is the compressor running the whole time? If so may have a problem with a refridgerant leak....check the compressor in the rear of unit, feel if its hot....may be as simple as a relay.

i dont think so i would look at the compressor kicking out on thermal overload or a faulty thermostat thermostats have two settings cut in cut out your cut in could be bad and not turning the compressor on till the temp reaches melting temps now if your hearing a click buzz then you need to look at the compressor and make sure the compressor fan is running but its not a defrost promblem

you have a refrigeration issue partner let her go 16 yrs. is good service you can replace it for 3 to 5 hundred the repair will be that IF you can find someone with the r-12. don't go for a top it off and go deal the food you lose is to expensive for that to be economical.