I have heard that an elongated Isuzu/Chevy Luv starter will only work on a pre engaged set up and will not work on the later verto set up.

I agree with you that this is a solenoid problem.

Does your car have the inertia or pre-engaged starter motor?  The inertia starter uses a separate, remote solenoid.  The pre-engaged starter has a solenoid piggy-backed onto the starter motor itself.

Chevy luv, hehe, they lasted about 2 years in Michigan road salt. Saw a really practical step side version in Oregon a couple of years ago, looked like new, would really turn heads here in Michigan.

you can easily replace the starter with the solenoid by purchasing the Chevy Luv starter. It requires minor slotting of the bolt holes and is only $38 at local AutoZones...

Took the solenoid off and you can hear it rattle.  Put a meter on the two large contacts and you get a short then rattle it and you get an open, guess that's the problem.  Just have to make sure I get the correct one when I order a replacement.

+1

It sure sounds like the contacts on the solenoid are frozen together.

Starter solenoid most likely stuck ON. therefore its sending current to starter

Don't know your exact setup.. perhaps a good wack on the solenoid could free it. but it also could have melted / Fused together contacts and be permantnly ON.

Stopped for a haircut on the way to the grocery store yesterday.  As a stopped at a few stop lights on the way I heard this buzzing noise.  Stopping in the parking lot I turn off the car and still this buzzing noise.  Opened the hood and listened and touched and found the starter was still turning.  Checked to see if the ignition switch was somehow still on but no.  

Fortunately a fellow pulling in next to me had some tools so I pulled the battery cable off the solenoid and it stopped.  When I touched it again the engine would start but the starter would continue to run, curious!