If heater comes on probably board. Thermistor is not likely. Press and hold colder and power buttons at same time for @ 5 seconds to enter service mode. Press colder button while in service to toggle through thermistor readings. Will exit service mode on own after @ 90 seconds.
S/Z refrigerators are known for evaporator leaks. Remove back panel. Evaporator will probably have mini volcanoes on it where Freon is leaking.
On freezer when coil is frosted over, press and hold ice button for @15 seconds to force defrost cycle. Heater should come on. If not check for 110v at heater and ohm out heater and bi-metal. If heater comes on problem is probably control board.
With refrigerator if Freon had to be added there is a leak and needs to be repaired or just going to leak out again.
Sounds like you need to blow out cond coils..It is going to make mess.I carry old towels to seal off compressor side best I can and use exhaust from shop vac. Baffle does force air down to drain pan so check pan if you are going to run without it.
I see in video ref side heat exchanger and compressor was replaced, was evaporator replaced as well? Can also see fre side drier has been replaced but ref drier passes by to quick to make out. Was it replaced ?
When you are checking burners check venturi tube coming into buner. You should not be able to remove it from burner body. Also it looks like there are after market drip pans in trays. Wolf says you cannot use them because they change air mixture.
Need serial number. Is the fan motor mounted horizontal under evap coil or vertical next to it. If under coil it sounds like defrost drain is freezing up and overflowing. Check wiring and trough and drain heaters.
Drain tube runs down back of unit. If water is freezing under drawers you have other problems. Even if water leaks under draws it shouldn't freeze in ref section. Insulation between ref and freezer is breaking down allowing floor of ref to get too cold. There is a heater kit for this problem. I will get part numbers for kit and hose tomorrow and post tomorrow when I get home.
When you take ice maker and trough cover off there will be a bi-metal you need to check while it is cold. Not main defrost bi-metal. If lower bi-metal is closed trough and drain heaters will need replaced.
Control board in unit should have part number on it. Should be a 7 digit number starting with 420. If you can find number you may be able to cross number and see what serial range it fits. By annuciator do you mean door arlarm/bell button? If you do not have alarm it is prior to 1800000.
Is ref compressor running when ref fan is off? Need to check for 110v at motor when it is not running. May be cycling off with cold control. If evap is good and unit is cycling off while warm cold control is bad.