Hey folks, hoping to confirm that what I have is indeed a dead starter motor on my '84 300TD Benz. I tried starting it today for the first time in two years and it was turning over (and clicking), but VERY slowly. I was jumping it while attempting to start it, so I assume the battery was fully charged and not a limiting factor.

I connected a 12.4v battery directly to the starter motor to test it, and it did not run. All I got was a clicking sound (I think the solenoid?) but no motor whir. You can see/hear it in this video: https://youtu.be/dyztJ4lOZk0

The car has been sitting for about 2.5 years. Before I parked it in Dec 2014 it was running/starting well, although the day I finally parked it it wouldn't start (I thought because of the cold - in Taos NM it was below freezing). I had one issue earlier that year (2014) where it wouldn't turn over at all and I jumped it across the solenoid by touching a screwdriver to two of those bolts. It started right up and no problems until the cold that December when I left it parked. I tried starting it once since then (probably winter of 2015) and it would turn over slowly but not crank fast enough to get going. Battery was fully charged and I plugged in the engine block heater before trying... still I was hoping the winter/cold was the problem.

Now it is summer so cold shouldn't be a factor. I'm back at it - this time I need it to run. Two questions:
1) based on the video do I definitely have a dead starter motor? Or is there some other reason the motor wouldn't run when connected directly to 12v? I'm also confused as to how the car was turning over this morning if the starter motor is indeed dead - is that possible? Do dying starter motors turn over slowly or does that indicate a battery problem?
2) if starter motor is dead, any thoughts on replacing vs rebuilding? I know there are threads/DIY guides for both options on this site, just curious about the benefits/costs of each option. I'm not a super experienced mechanic and it seems like most people replace.

many thanks!