At best you have a faulty PSU cable (Kettle Plug) or wall socket.
More likely, you have a faulty PSU (Power Supply), they're practically consumables. The cheaper they are the less efficient and less long they last.
(A 650W PSU is under spec for your rig - it will be at a high load, so it will be running above its ideal temperature range.)
Another possible is a faulty motherboard, which is routing the power. Less likely, but most annoying if it's the case.
You need to get your hardware checked by someone who know's what they are doing basically.
Edit: Overheating possible to, you may have an extremely dusty PC.
You should use canned air or an air hose to clean out your PC, if you have never done this before especially so.
You need to pay attention to the airflow near your computer as well, for example if your computer is in an enclosed space or near a hot object like a TV.