I cannot find any info on the given model number.
Tried here and the Frigidigaire site

Please check it.

When you say the evaporator coils were frosted over, where they frosted/iced to the point that the evaporator/freezer fan could not pull air through them?
This would have then been a defrost problem.

Is the compressor cycling or is it on all the time (other than when it goes through a defrost cycle)?

If cycling then it could be a control thermostat problem.
Note I do not know if this unit is electronic or uses an analogue thermostat.

If the compressor runs continuously:
Check that the evaporator fan is OK.
Remove the cover in the freezer so you can check the evaporator coils.
If they are heavily frosted over then you have a defrost problem.
If there is just frost in one area of the coils (usually where the freon enters them), then you have a sealed system problem.

You can usually hear when the compressor is on.
Also on most units the condenser/compressor fan is on whenever the compressor is on.

Yes it does sound like the original problem was a defrost problem.

Best to pull the cover in the freezer and inspect the evaporator coils so you can see what is going on.
They should have a nice even coating of frost.

[COLOR="Blue"]The compressor and fan are both running and appear to run continuously.
Should they cycle on/off?[/COLOR]
Yes they should cycle on/off when the unit reaches the set pointy temperature.
Since the unit runs continuously the control thermostat is OK.

Since the compressor runs all the time it is trying to reach set point temperature but cannot therefore is sounds like a sealed system problem.

This will be an expensive repair as you need a pro. In most cases it makes more sense to put the dollars towards a new unit.