Your obviously getting enough air flow to close the sail switch if it fires up.
I would start by removing the flexible supply duct and checking the air flow, checking that there was no restrictions.(lot of air will come out if disconnected)
You said you heard no difference between high and low fan speed, your fan motor shaft lube may be getting dry causing the motor to slow, this happened on my AC last year. I kept running it (about 3 days) until it finally locked up.
Either of these could cause the unit to cut off from an internal over-temp thermostat.
If it had adequate air flow, fired up but didn't put out much heat, I'd look at restrictions in the burner.(Dirt daubers, mice)
Good luck.