[COLOR="Blue"]Question, Let's say that the compressor is running constantly, and lets assume that the system has a reasonalble amount of Freon in it. If the cold control/cycling switch for the compressor has failed I would still receive air but wouldn't get cold correct?[/COLOR]
No. If the compressor is running then it should be cooling.
The cold control turns the compressor on/off. This is what regulates the freezer temperature. There is nothing in the sealed system to turn the freon on/off it is a closed loop system.

[COLOR="Red"]Question: Does the compressor work as designed?[/COLOR]
Cannot say but it is running. The problem may be in the compressor

[COLOR="Red"]Question: Is there enough Freon in the system?[/COLOR]
Only a pro can tell by attaching gauges to the unit.

[COLOR="Red"]Question: Defective T-stat or Timer?[/COLOR]
I doubt i. The compressor is running. It should be cooling. The problem is in the sealed system.

[COLOR="Red"]Question: If the compressor works but is not cycling correctlyto compress the liquid into gas, is the internal system i.e. Condenser cloggedinternally, the compressor bad or is the cold control bad causing thecompressor not to cycle correctly?[/COLOR]
Could be a clogged orifice in the sealed system.
If the cold control could could fail by staying closed all the time, the compressor would run continuously but the symptom would be that the freezer and fresh food sections would be too cold.

You have the way the fridge works backwards.
Here is a good link explaining how it works.
http://www.acmehowto.com/howto/appliance/refrigerator/overview.php

[COLOR="Red"]Possiblecauses: Compressor failed, cloggedInternal condenser, Cold Control failed, Little or no Freon in the system.[/COLOR]
It is not the cold control.
Could be any of the others but you need a pro to fix it and it will be expensive.

[COLOR="Red"]Question: If there is little or no Freon in thesystem then why can I hear liquid running in the coils in the back of thefreezer?[/COLOR]
You may have some freon just not enough. Also it may be the compressor oil.
It is not normal to hear gurgling.

[COLOR="Red"]Follow-upquestion: If there is little tono Freon in the system why would it freeze the back coils prior to the replacementof the T-stat and Timer but now it won't get cold?[/COLOR]
This I cannot answer as I do not know.

[COLOR="Red"]Question: If the cold control unit has failed, whycan I turn off the compressor by turning the switch to the off position?[/COLOR]
Yes but you are manually opening it's contacts when turned off.
When on the freezer temperature opens the contacts when the freezer reaches set point. Since the freezer never gets cold, the contacts never open and the compressor runs all the time.

[COLOR="Red"]Question: If the compressor has failed, why does it continuallyrun unless unplugged or turned off by the cold control switch?[/COLOR]
A compressor is a an electrical and mechanical device.
The electrical (the motor) can run but the mechanical (compressor head and linkage) may have failed.

[COLOR="Red"]Question: Does not having the back panel installedaffect the internal temperature inside the freezer?[/COLOR]
It can because you are changing the way the air flow works to cool the condenser coils. But the evaporator coils still should get cold.