Trane XL 1200 - Blower Not working - where to start?

Turned on my AC for the first time this year today, and wasn't getting any movement of cool air. Initially, it seemed like there was some cool-ish air flowing through the registers, but after a half-dozen hours the house was just kind of muggy. Air was flowing through the registers without much force, and it didn't look like the fan blade inside the unit was moving. It's too late tonight now to go out and try to see if the blade can be turned, but I thought I'd check here to see if there are any logical "next steps" or things to check before I call a pro.

When I turn the unit either to the "Fan" or "Auto" position on the thermostat, something inside the unit turns on...don't know whether it would be the compressor or if there's something else in there. But in neither position does the fan turn on. I just turned the breakers off and then back on and tried the thermostat in both positions, but all I ended up with was the same issue...this time I went outside, and the unit had gotten quite warm in the 5 minutes that I had it in the "Fan"/"Auto" positions. It's almost like something is getting bogged down and can't move...hope I didn't burn anything out that wasn't already burnt out!

This unit worked fine last year for the half dozen times that we turned it on over the course of the year. And then it sat idle until today. I've not done much of anything HVAC, but I catch on to things quickly and would be willing to try things if it'll save me on repair call costs (and learn a thing or two in the process).

Any tips?

Is the blower in the air handler rotating or not?
Is the fan on the condensor unit rotating or not?
Is the compressor running or not?
Do you have a volt/ohm meter to troubleshoot the system?

I think the compressor is running (or at least it sounds like it is). The large fan near the top of the unit (not sure what it's called) doesn't appear to be running. I do have a multimeter I could use to troubleshoot, if I have an idea of what I need to be looking for.

Thanks!

Just checked this morning, and it appears the blower fan (large fan at the top of the unit) moves smoothly when pushed by hand. Might this be an issue with the blower motor?

Not to offend you but, this is very hard to do online when you are unfamiliar with the components involved.
First off, we need to make sure if the compressor is running or not. We also need to know if the air handler blower is running or not.
To see if the compressor & fan work, you will need to manually engage the contactor on the compressor unit. You will have to remove the panel to gain access to the contactor. Press down the button in the middle of the contactor to manually engage it. Make a note of what comes on and what doesn not come on. The compressor and fan should both come on. To see if the air handler blower works, you will have to remove the panel from the furnace, hold down the safety switch with tape and jumper the "R" & "G" terminals where the thermostat wires connect inside the unit (on the control board). This should unconditionally engage the air handler blower motor.
With the thermostat set to A/C and setpoint below actual, you will want to test the voltage on the control wires to the contactor and should see 24VAC. You should also see 24VAC between the "R" terminal and ground, and the "G" terminal and ground when the thermostat wires are not jumpered. After seeing the results of these preliminary test, I will know more as to what to check next or advise as to what may be wrong.
Good Luck.