Burnt out lights in modules and gauges is very common. Doesn't affect operation, just annoying. Most of us just take them apart and replace with LED's except the manual ones are a PITA to take apart because of those slide knobs.
Getting a new one would probably not be any better since you would have to take it to a dealer or someone with a Tech 2 to program it. These are not high failure items but not unheard of. If mode isn't working and two different control heads didn't fix it, likely it's the actuator. The A/C not lighting might be either because it's too cold or the system is inoperative because it's empty of refrigerant (but not sure of that).
I sent back the control unit today for an exchange simply because the ebay seller said everything was testing and working yet the lights did not work. So I'm getting a different used replacement unit mailed from them. As you mentioned @Mooseman, prior to this, changing the control unit will probably do nothing but I figured might as well have a backup. I also ordered brand new ac delco defrost, mode, and driver's side temperature actuators from amazon and they'll be here this Wednesday. If they don't work I can always return them. Love that about Amazon. I did find the passengers side actuator and when I moved the temperature slider the white circle on it didn't move at all so it will probably have to be replaced too. I'm sure the refrigerant will need to be refilled but it should still work. Last time I used the a/c it blew cold air just not that cold.
Fixing this HVAC issue should have taken literally like a day at most but you gotta realize that I know nothing about vehicles and it take time to research and test a possible solution. It's been a great learning experience for me thus far to fix these issues with everyone's input and I really appreciate all your guys help! I wanted to start by testing each part before replacing but it would require me to end up buying a tech 2 clone with a xp laptop which would cost $400 easily vs simply buying 3 actuators off amazon for $130. If those actuator's don't make a difference then oh well I'll just try a different step. The resistor pack for the fan speed 5 only cost $30 and it worked perfectly. I did test the old resistor pack and it didn't click like the new one did when I applied 12v to it with the power probe. So that confirmed the old one was bad. Working smarter not harder means having the right tools to test each part before replacing but since I don't plan on working on thousands of vehicles it's better in my situation to use the part shotgun and take action vs inaction. I take inaction by spending too much time overthinking and not actually trying to replace anything.
So to sum this up, from day 1 here I should have just started applying your feedback replacing parts since there was enough evidence that the most likely culprit were the actuators. Sorry to make such a long post on these forums but now I'm more confident about the solutions to this.