Either your PSU doesn't have enough juice to support the 3650 or the second card doesn't work either. I would lean towards the PSU as being the issues since you are on your second GPU already.
Do you still think its the PSU - because when i had the card originally (the 3650) it ran perfectly for a few months....
How long do PSU's usually last because mine is the original - made my machine custom when Windows XP was brand new almost a decade ago
I give my PSUs a 5 year lifespan. I overclock so they take a bit more abuse than average though. I've personally had PSUs work for 15+, but by that time they are usually in an internet only PC that I gave to my family.
You have 2 options to be able to tell which is causing the issue. If you knew someone with an older PC where you could install the 3650 to tell if the second card is bad or you could get a new PSU to see if your PSU has weakened over the years.
It's really a toss up and you just have to try something to be able to tell. It's also possible that both the PSU and the original 3650 when bad at the same time.