@JohnnyBlu84Ah, I built computers since 2000 and a gamer. The first thing you can check is the power button when the computer is on press and hold it until it turns the computer off, When the computer turns off it should spring Back, if the power button is not all the way closed it could be accidently telling the computer to shut off when you play the game. Also since a new power supply was recently installed if it has modular connections make sure the all power connections to the power supply are secure and tight, also power connections to the motherboard need to be secure and tight. A 4 pin power connector that connects near the cpu must be connected or some motherboards will put a kill switch to the power to protect the CPU from damage. Also make sure if you have a dedicated video card that has power connectors make sure you add the special pci-e power connectors either 4 6 or 8.
If you have no idea you can always take it to the local computer shop and they will check out the system for you.
Always unplug your system when working on the inside of the pc from everything including power, monitor and eathernet lines.
Edit: I almost forgot check the case panel connectors on your motherboard to make sure though wires didn't slip out they can cause problems like that if not all the way in.
Edit: I fixed some missed words in my first sentence my keyboard is getting on and tends to skip keys sometimes.