Sounds like you have a sealed system problem.

You said there was frost only at the top of the evaporator coils and the compressor is always on, this would be a symptom of low freon.

On a good fridge the frost should be a fairly even coating over the entire evaporator coil. This should be checked after the unit has run for several hours without a defrost cycle.

The frost is usually where the freon enters the coils.
Here is a link, see the three example pictures part way down the page.
http://www.applianceaid.com/frig_notcold.html

If it is low freon it will be an expensive repair as you will need a pro.
Also there is no use putting freon into it until the leak is found and repaired.

Usually it makes more sense to put those dollars towards a new unit.