Thank you for your inquiry.
I don't think it could be the power jack, otherwise, you won't be getting any power with the PSU after all.
To my knowledge, it could be the aging battery that can no longer output enough amps for the laptop that lead to random shut offs during gaming.
In the end, the battery dies eventually? Just my guess with the limited information. If you are unsure what to do next, I would suggest to send it to your nearest service center for a check up. Our engineers will help you diagnose, thank you