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I am assuming that the compressor runs continuously other than when the unit goes through a defrost cycle.

Remove the rear cover in the freezer so you can inspect the defrost coils.

If they are heavily iced/frosted over you have a defrost problem.
It should be fixable for a reasonable cost

If there is only frost in one area (usually where the freon enters the coils) then it is a sealed system problem. This would be an expensive repair as you need a pro. Often it makes more sense to put the dollars toward a new unit.

Be sure to do the check after the compressor has run for an hour or so. If you check it shortly after a defrost cycle then you could reach the wrong conclusion.

Below is a link. Take a look at the example pictures about half way down the page.
http://www.applianceaid.com/ref...ator-not-cold-enough.php

Perhaps it is just the angle of the picture but the defrost heater does not seem to be in the correct position. Looks like it is not parallel with the back of the freezer and I think it should be.

When you first opened it up you may have been in a defrost cycle and that is why the compressor and fans were off.

The ice at the top does look like a sealed system problem but I would try to confirm this.
Unplug the unit, take a hair dryer and melt off all the ice at the top. Just be careful that it does not overflow the drip pan under the unit.Perhaps mopping some of it up will help.

Then put the cover back on and let it run for an hour or so and reinspect the coils.

If there is frost just at the top of the coils then I would say it is a sealed system problem.
It will be an expensive repair and often it makes more sense to put the dollars toward a new unit.

I would say this is a sealed system problem and will be an expensive repair.

You are welcome.

Just too bad the end result was not better.