I have a digital extension (1106) on a Starplus system that goes to a busy status when the phones not even in use. Once in this state, the user has to clear (picking up the handset & placing it back on hook) the phone. After 4-5 min the phone goes to a busy state, beeps away, and doesn't return to an on hook status unless you "clear" the phone. It's as if the phone goes offhook and times out on its own.

Any thoughts?

Sticky hookswitch, the phone is not hanging up all the way, could be switching to speaker on its own. You could try a little contact cleaner and work the hookswitch a few times.

I replaced the desk set with a completely different one. Trouble followed.

You may have a port that is locking out, reset the system, there is a reset button inside the unit, top left. Do this without powering it down.