My radio doesn't work (the LED comes on but it doesn't make any sounds), and there are lots of 93 head units on the market for cheap. Is this a direct replacement for the one in my '90 GT?
That depends on which stereo you have and which one you want to plug in, specifically. Do you have the standard 4-speaker setup, or the 6-speaker deal (with speakers in the doors)? If you have the latter, then you currently have the "premium" stereo.
There was more than one stereo available as a factory option during those years. Mainly, there was a "regular stereo" and then a "premium stereo" (and there was a CD player optional in '93 models, which I believe would also fall under "premium) - one used 4 speakers, the other used 6 speakers and a separate amplifier. You can't plug the harness from one directly into the other, as not all of your speakers will work. It has to be a standard to a standard or a premium to a premium.
To eliminate any confusion, just buy a wiring harness appropriate for your application and then plug in any aftermarket stereo - less hassle, costs just as much (perhaps even less), and WAY better sound. Unless you're absolutely positively hardcore anal about having everything look stock, there's no real reason to bother dumping another OEM stereo in there, IMO.
Even if it is premium to a premium, it may not be plug and play if all the components are not the same year... I am learning this the hard way. If I was not so hell bent on keep the 7up car "factory looking" with no new holes or cut harness, I would just put in an aftermarket.