VW Jetta Wagon 2001 Randomly won't start

2001 VW Jetta wagon will randomly not start it up. Jumping it or popping the clutch doesn’t get it going. I’ve made sure there is nothing draining the power and the battery is new and clean. My mechanic has run diagnostics on it to check the codes and kept it for a week to use it when he ran errands; it never gave him any problems. He wants me to give him a call if I get stuck again so he can hear what it sounds like when it won’t start. A week later, it wouldn’t start for me(of course it was on a Sunday). I waited an hour and it started. It does this whether it’s been sitting over night or after using it for an hour or two. I’ll go somewhere, park,and return 10 minutes later and it makes that sound like there isn’t quite enough power to start (starter is new).
Now it does have over 382,000 original miles on original motor, timing belt replaced a few months ago and the mechanic said it’s clean and strong. I would love to know what to do other then getting rid of it! Thank you!

@Parma‌

When it doesn’t start . . . it at least cranking over?

If it is cranking over, does it crank over slower than usual?

Here’s something to try, when it doesn’t start . . . slowly cycle the key on and off a few times

if that does the trick, you’ve most likely got a fuel pressure problem

Are all of your battery connections clean and tight. When I mean all of them, I literally mean all of them, all the way from the battery to the starter, and the ground straps also

“I’ve made sure nothing is draining the power”

No offense intended . . . but unless you’ve performed a parasitic draw test, no, you haven’t made sure that nothing is draining the battery

I know the battery and starter are new, but have they been tested. Occasionally, you’ll run into a bad new battery. Or a starter which is no good. By the way, the “new” starter you mentioned may very well be a rebuilt. It’s quite common

Is it slowly turning the engine? I would double check the starter connections. Also, make sure the starter bolts are tight. Starter uses its bolts and contact with the engine for ground.

If it isn’t cranking at all when this happens — no rrr rrr rrr sound with the in “start” – try cleaning and tightening the battery connections. That would be a good place to start.

How old is the battery by the way?