Here are your parts
Parts for Frigidaire FFU1764FW5 Freezer - AppliancePartsPros.com

Here is the tech sheet.
http://manuals.frigidaire.com/p...df/StCloud/297082201.pdf

[COLOR="Blue"]The light is on.[/COLOR]
If this is the interior light, does it go off when the door switch is closed?

[COLOR="Blue"]The compressor gets warm and is running from what I can tell but only warm air is blowing in the unit.[/COLOR]
I am assuming that you felt the compressor and it is vibrating.
If yes and you have no cooling at all then it is a sealed system problem. his will be an expensive repair and often it makes more sense to put the dollars towards a new unit.
I am assuming that the compressor runs all the time except when it goes through a defrost cycle which occurs every 12 hours or so and lasts 30 minutes.

[COLOR="Blue"] I replaced the defrost thermostat just because that seems to be the most replaced/ordered part but that didn't change anything.[/COLOR]
Even if you had a defrost problem (evaporator clogged solid with ice/frost) the fan would still blow cold air. It just would not be cold enough to cool down the freezer compartment enough.

[COLOR="Blue"]The compressor relay isn't making that clicking sound and I removed it and it does not sound like some of the broken ones sound I've seen in videos.[/COLOR]
If the compressor gets warm and is vibrating then it is running so the problem is not the start relay.

[COLOR="Blue"]What should I be checking for next?[/COLOR]
You coud check for frost on the evaporator/freezer coils but it sounds to me that the unit hs a sealed system problem.

[COLOR="Blue"]Then you're leaning towards it being low on freon meaning it has a leak which pretty much means replace it since it's 8 years old?[/COLOR]
Unfortunately, yes.

I am not sure as I do not have a wiring diagram for this particular unit's compressor.

If the compressor is running all the time except when the unit goes through a defrost cycle and it is not cooling then it is not a relay problem.

The relay can only cause two problems:

1. The compressor will not start.

2. The compressor overheats because the relay does not disconnect the start winding. The compressor then will short cycle as the thermal overload kick in and out.