[COLOR="Blue"]What can cause malfunctioning of the cooling system?[/COLOR]
Below is just for the sealed system itself.
There are a bunch of reasons just a few would be:
A leak and you are low or out of freon.
A clogged orifice.
A mechanical problem in the compressor.
A compressor start device problem.
An electrical problem in the compressor.

[COLOR="Blue"]How does one determine if it is the defrost timer verses the compressor?[/COLOR]
Easiest way is how you did it.
In both the below the compressor should be running continuously as the unit tries to reach set point.

If the coils are heavily iced/frosted over to the point where the evaporator fan cannot pull air through it, then you have a defrost problem.

If the coils only have frost in one area (usually where the freon enters the coils) then you have a sealed system problem. This will be an expensive repair as you need a pro. Often it is better to put those dollars toward a new unit.
Be sure that the unit has run for several hours when doing the check. If you do it shortly after a defrost cycle you may arrive at the wrong conclusion.