Wow, sure sounds like one of the original 1989-era five-band radios.
How many bands are on yours? This will narrow down the age.
The oldest Saturn models will tend to have the longest laundry list of faults when they get past the 20-year mark.
Once it's old enough to buy a drink, we see a lot of them with toasted final transistors. The final transistors' metal tabs that bolt to the aluminum heat sink will be a dark, flat black color. This is the metal oxides that build up from excess heat. The habit back then was to "turn up" the bias adjustments, and cause excessive heat to cause the two finals and sometimes the driver transistor to fail.
The added current load to the final transistors has to pass through the modulator transistor. Some folks like to call it a "regulator", since it also controls the radio's carrier power in AM mode. This is what it looks like. Frequently the factory would leave off the white heat-conducting compound that fill heat-blocking gaps under the white insulating washer.
When those radios were being sold new we learned to unbolt these parts and add the missing compound. Even then we had plenty enough volume of repair work that we didn't need to send suicidal radios home with a customer.
Do you have a wattmeter?
A dummy load?
A multimeter to make DC-voltage measurements?
An oscilloscope is an unfair advantage, especially if you have learned how to use it.
It does permit you to do a sort of sideways "in-circuit" test of a final. A common failure is for the connection between the base and emitter legs to become an open circuit inside the transistor. A 'scope will show a much-higher RF voltage feeding into a blown final, since the input pin can't absorb the drive power when it's blown out.
But you need to know what the waveform looks like when the part is good for that reading to inform you about this.
Easiest quick test is to unsolder the base lead of each final and (GENTLY!) stand it up away from the foil pad on the pc board. Try not to bend the lead directly against the plastic body, or you may break it off from fatigue stress. Ground the negative lead of a typical digital multimeter. Ground it to the circuit-board foil ground, and *NOT* to the metal chassis. Select the "continuity" or "diode" test. Touch the now-isolated base lead with the red probe. Should read between 6/10 and 7/10 of a Volt. If it shows no change when you touch the probe to it, that one's dead, Jim.
73