I recently decided to upgrade my PC for some gaming. It is an HP ProDesk 400 G3 MT. I did my research to find out what I would need and what would be compatible with my motherboard. I decided to get a GTX 1070, and a new PSU since the stock one was only 180W. I got the Corsair CX550M today and started putting it all in.

Now after plugging everything in and turning the computer on, it turns itself off. Sometimes immediately after powering it on, sometimes after a couple of minutes. Sometimes I would get a bluescreen saying that "Windows hasn't loaded correctly" or something like that (translating from Swedish), and sometimes I get all the way to the desktop menu before it shuts down.

The PSU also makes an electrical noise most of the time, but not always. This is how it sounds: https://www.dropbox.com/s/q7ymxlm6vbddkya/PSU%20crackle...

In my troubleshooting I have tried:
-Unplugging both the HDD and the Graphics card completely to rule them out.
-Taking all the power connectors out and plugging them in again to make sure they sit correctly, multiple times.
-Turning on the computer while the PSU is outside the case.
-Reinstalling the old PSU, and it works fine (took out the GPU of course).
-Googling a lot.

Should I just assume that I got a faulty PSU and get another one?