A stronger Power Supply Unit (PSU) would make my Graphics Card better?

You should still be able to play your games with your new power supply unit. The power supply unit distributes the electricity through your computer. I would try to run my games the same it should not affect them. Also I would keep an eye on your computers temp. If it overheats then the fans in your computer are failing and you should get them replaced but I don't think that is it. I think your computer was trying to use more power then the supply unit would distribute then it would cause power failure to some parts of your computer in this case it was the fans. Just continue playing your games the same with the new PSU and keep an eye on the heat of the computer because it might not be the power supply.