Started to overheat turned off engine now will not start

Car was working normally, no issues of any kind. I noticed the over heating sign and stopped immediately. I tried starting the car and it would not start at first try. Before I could start the car again, the mechanic removes the battery head to tighten it properly.

Before fan system was dismantled and changed (which got the fan working faster and finer than before), I noticed that the car would start then stop after a few seconds without putting it in gear.

After the fan was installed, I noticed the car would start when not in gear but as soon as it's on drive or reverse, it jerks and stops.

An urgent response would be appreciated.

Note: In my country, most mechanics do a lot of guess work. The few automobile centres with full diagnostics will have you pay through your nose to check what is wrong first before they can start working on the car. I just said this because I may not have access to a proper diagnosis