TURBO DIESEL ENGINE RENAULT LAGUNA 1.9 99`

Here's my situation:
I was driving my 1999 Renault Laguna Turbo Diesel 1.9 when it suddenly shut off as if I'd turned the key to turn it off (it kept rolling). I tried to start it; the engine turned over but wouldn't start. Then, about a minute later, it started. I drove another 100 meters and the same thing happened again. From then on, I couldn't start it at all.

A mechanic told me the injection pump gear had come loose. Is that possible? Should it have made any unusual noise? I didn't hear anything. Later, at home, every time I tried to start it, the starter turned, and it all sounded normal, but the engine wouldn't start. The strange thing is that it stalled, I was able to get it started again and drive another 100 meters, and then it stalled again.

Also, does the injection pump gear connect to the timing belt or the air conditioning belt? He says that's why the engine timing is off, and now there's a problem with the valves.

I look forward to your comments, thank you.