2013 VW Jetta occasionally won't start, but will turn over

Background

• 2013 VW Jetta S 2.0L
• Serviced regularly by the dealer, as per the guidelines, and recently had a major service (e.g., spark plugs, filters, etc.)

Incidents

1. When I came back to my car after it had been sitting for a few hours it wouldn’t start. It would turn over, but wouldn’t get running. Someone gave us a jump start and that solved the problem. Since the jump start solved it, I assumed that it was the battery, which was about three years old, so I bought a new one and installed it.
2. The new battery seemed to solve the problem, but then after a week it wouldn’t start again. I asked my neighbour for a jump start and by the time he arrived it just started by itself.
3. It then ran fine for two weeks and just now my wife had a similar experience: the car was sitting for an hour after running fine then it wouldn’t start. After leaving it for a bit, it would start just fine.

Question

Prior to the last incident, I booked it in with the dealer for them to look at it, but couldn’t get in for two weeks. Of course, I cancelled the appointment after it ran fine for two weeks and then it crapped out again. I guess I’d have to wait another two weeks just to get it in. Regardless, they were not confident they could identify the problem since it is so intermittent and I don’t want to drop some cash on a shrug. Is there a way I can narrow down the problem myself?

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Update

Cleaning the connections hasn’t solved the problem and the multimeter reads around 13.98 – 14.40 when the car is running.