Question PSU clicks, PC turns on and off. Do I need a new power supply?

[Primiean]

My PC has been having an issue where the PSU will click on with the PC and click again and turn off the PC. This started when I tried to add a hard drive (the PC was off when I did this). After plugging in the hard drive the PC would no longer turn on. Fiddling around and undoing everything didn't work, so after setting everything to how it had been I put it back resigned to try again later. When I put the pc down I dropped it about an inch, and it started right up on contact.
Since then, the PC will occasionally have the same problem and the only way I can get it turn on is to drop it a little bit. Obviously this is not the way to start a computer.
Any ideas as to what's going on?

 

[SgtScream]

Check and reseat all of the internal and external power connections of the computer.

 

[Metal Messiah.]

Please kindly provide FULL PC specs as well....What's the make and model number of your Power supply unit/PSU ? Without knowing the details of the system which you are currently using, it's kind of hard to troubleshoot such issues.

List the PSU model/brand.

 

[Primiean]

Please kindly provide FULL PC specs as well....What's the make and model number of your Power supply unit/PSU ? Without knowing the details of the system which you are currently using, it's kind of hard to troubleshoot such issues.

List the PSU model/brand.

PSU is a cooler master 750W
CPU: i5 6600k
Motherboard: MSI Z270 SLI Plus
GPU: GTX 960
SSD: SanDisk 480gb
RAM: Kingston Fury 8gb