I took a look at the service manual for those, and didn't find anything useful.
Could be any number of issues, maybe someone who owns one could shed some knowledge on it.
Usually when a radio is acting like that, it means it's either trying to do something it can't, thinks there is something wrong, or it's reacting to something.
A few things you could check:
Make sure none of the buttons are jammed. A stuck key could do this.
Make sure the battery is actually good. These are older radios, so a "new" battery might have sat on the shelf a long time. Check the output of the battery with a multimeter.
Short of that, you'd need some test equipment and the programming cable to go much farther. Could be the VCO has unlocked, either due to programming error or failing components. Only way to know would be to have the test gear and manual.
But, putting that much work into a radio this old is kind of pointless unless you want the punishment.