The cable is either stripped, or not connected.
It's not hard to remove the headliner and check it out, just watch for the A-pillar covers, they can crack pretty easy given the age.
Something else you can check, is the manual override, it's near the hatch, has a little plastic cover in the headliner, pop it out, and use an allen wrench to turn the wheel. If the sunroof moves, then the cable is hooked up, but if it doesn't, that's the problem. You shouldn't be able to move the sunroof by hand in any event.
For 1st Gen CRXs, don't, under any circumstances take them to the dealer. None of the techs there know what to do with something that old. You're far better off taking it to an older car shop, or doing it yourself.
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-Harry
AIM: NDcissive
CRX and Pre '92 Civic, Engine Tech and Tuning, & Track and Autocross Forum Mod