Car won't start
 

Hello fellow Mini Peeps. Yesterday I drove my car for about 30 minutes, turned it off for about 5 minutes and when I went to start it, it just clicked.
I had full bright lighting inside and out like normal.
Someone approached to help and we tried giving the car a jump straight to the battery and just got the same "click". Then we tried jumping it via the engine compartment and it started no problem.
I drove the car 100 miles and about 2 miles from my destination dash lights came on and headlights dimmed.
Had AAA check my charging system and result was, battery good and alternator overcharging at 16.1- 16.2 volts.
I installed a new alternator and new battery and then "click"!! It'll start only if jumped through the engine bay and not if jumped directly through the battery.
Please help!!!

I'm not an expert - but just a thought - possibly a connection issue at the starter itself?
It's (starter) a PIA to get to but might be worth a look before throwing parts at it.?