Pretty much what the title states, I have a Bryant gas pack that operates like normal when it is in cooling mode, but once the thermostat calls for heat, the system shuts down completely. Even the fan doesn't work. Can anyone list the possible reasons this would happen?

Just to clarify, neither the outdoor fan nor the indoor blower operate in heating mode and as far as I can tell, nothing operates at all on the system outside. I know the first step would be to check power at the thermostat. I wasn't too sure what to check, but considering the heating mode was the only one that wasn't operating, I checked to see if voltage was being supplied to the W terminal on the thermostat, which controls the heat relay I assume, and voltage was being supplied to it. Now I just to know where to go from there if I did that right.

Your fan motor in squirrel cage has 2 or 3 speeds. The high one is for ac and the lower one for heat. Check the contact, wire, and fan. If the fan doesn't run, your unit automatically shuts the burners off. I had the same problem and it stumped a lot of people except for an hvac guy I worked with. He had to replace my motor cause the low speed contacts were burned up.