Yes check Both Fuses.
1 is "backup" power to save setting, keep time w/ I-key Off, etc.
2 is main power to run the whole thing.
But seems both are OK when Clock runs & correct turning I-key On.
Old Radios have Hundreds to Thousands of solder joints & any can fail killing part or the whole unit. Then have capacitors etc that "die" just from old age, worse when Parked outside where Cabin Temp can easily reach 150 to 200+°F. See
https://www.fiero.nl/forum/Forum2/HTML/141784.html Fiero Engine bay vs Heat.
Is part of why can't get good used or "Rebuilt" radios now. "Good" Used radio may work now then die in days to weeks later. Even if can find good "cores" the rebuilt co's have to do a lot of work for little profit just to have product that last 30-90 days warranty.
For that matter, I have some good radios that "died" just sitting in storage & @ lower temps that in a car. So even Garage Queen Cars are not immune to this problem.
Even when you "upgrade" to fit newer GM units in 90 to early 2000's, most of them are 20+ years old too & have same problems. 2 of my dead radios are later model units that worked when I got them.
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Dr. Ian Malcolm: Yeah, but your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should.
(Jurassic Park)
The Ogre's Fiero Cave