If it's (dumb supposition, on my part) a Made in China, the way most people repair them is through throwing them away. If it's a quality item, let's suppose, what exactly is malfunctioning?
Looks like the EJECT button is dejected. Go around, look for another CD unit exactly like it; failing that, look for one where the CD drive gave up the ghost but the front face is still good, and swap them, or take it to someone who can swap it for you.
If 80's then at the very end of the 80's, at best. It looks like a much later model unit placed in an 80's vehicle
That's possible. Some of the Chrysler sound system connectors stayed the same from the mid-80s through about the very early 90s, when CD players began to show up.