Radio/Clock problem

My son picked up a 1983 Coupe with 64K original. My question is the clock works when you push the button on the radio but once you release the button the clock fades and the radio won't come on. Is it best to just buy a aftermarket or is this a easy fix? it's a (radio cassette player) http://www.automotiveforums.com/vbulletin/images/icons/icon6.gif

This is a Delco deck with a digital (orange LED) display, right?

EVERY one of those I have seen in the past 15 years has been broken, usually related to a malfunctioning display and related circuitry.

IMO go for a new one. Finding the problem and repairing it in the old one would be exceedingly difficult and not worthwhile, unless you think the car is a contender at Pebble Beach.