300-E starter
 

Clicking sound when starting for about a week - would not start one day and then started the next day. Replaced the starter, hooked up, car started 3 times with some clicking during start. Starter motor then continued to run and would not shut off with key. Bendix not engaged to ring gear, had to disconnect battery. What are possible problems? Starter? Other?

It's unfortunate that folks immediately associate "clicking" with a faulty starter. Often times they assume the solenoid is bad.

It's too late now, but next time, pull the battery if the car is down and take it to a shop and request a load test be performed on the battery. Another mistake folks make is performing an open circuit voltage test and assuming that if the battery read 12.60 or better that it's OK. Not so. I've seen batteries read 12.80 or better and flunk a load test.

Perform a load test on the battery before assuming the solenoid is bad.

Running again, oh boy!
 

Thanks for advice I think. Had battery load tested as per your advice. Took remanufactured starter back off car. Reinstalled original starter.Super-cleaned battery terminals, carefully reassembled, and it seems ok. About 170k miles on this car. Purchased from MB dealer with about 120k. Great service from this car so far.