don't know anything about the sport, but will offer some suggestions:
yes, check/swap relays.
On the trac, see one of the first posts with user manual, it shows relay 55 for the blower motor, -no idea if it's the same on the sport.
I would also suggest checking the blower motor resistor, but you say it works at no speeds, so it's probably not that, should check it anyways, could be a rusty connector.
Don't replace things randomly just because it worked for someone else, always check to make sure what you replace is really broken.
you probably could have measured to make sure the motor was getting power with the meter before replacing it, and applied power manually to it to see if it runs by itself - could have saved $40ish dollars.
If it was getting power and not spinning, yes the motor may have be broken.
Techs don't charge $100+/hour to guess, it's for properly diagnosing problems (well maybe they do for educated guesses when stumped).
85TA in your case, the switch/fuse/relay needs to be checked, probably only the relay left to check - look in the user manual for your truck so you know which fuse, relay to check.
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