The clicking, sounds to me, could be the electrical relays by the fuse box. Get a hammer or something and bang on the starter a few times. DON'T BEAT IT !! Could be the starter drive/solenoid could be stuck in place or jammed. I had to do this a few times on my 240D before it was buried (RIP).
Check the other ground strap that attaches to the bellhousing of the tranny on the driver's side. Better safe than sorry. All else fails, take the starter out and go to a parts place. Some of them still test starters and alternators.
99 C230K Sport