kioskhill45

It's sounding like the PSU is losing ground to it, making it just cut off.
I'll explain the basics of it.

What I mean by that is PSU's have a single green wire in the 24 pin ATX plug (Main plug), that wire is used via the motherboard to control whether the PSU is on or off. If it loses continuity to ground the PSU will simply cut off with no warning.
The PSU uses ground being make or broken to turn the unit on or off and the motherboard is what normally controls this.

You've described it as just cutting off with no BSOD or anything else, one moment it's on and then it's just off and a problem with the PSU losing continuity to ground via the green wire will certainly make that happen. 

You may have a problem with the board maintaining this connection, iffy/sticking/bad powerswitch in the case or perhaps it's a grounding problem with the board itself. 
Be sure the board is securely in place in the case, nothing loose with the screws and that you have enough of them. I'd suggest at least 4 or more mounting screws to the board while it's in the case to know you have enough grounding capacity to keep it all running.
I'm ruling out things here such as thermal trip with the PSU since you've already swapped it and the system still has this problem.

That's what it's sounding like to me.

So....
Check your screws and where they go to see if they are tight and the metal rings around the mounting holes are clean, not rusted or corroded... That kind of thing because that can and will cause a connection problem.

While it's VERY unlikely for this to be with two different units, make sure the green wire in the plug itself isn't loose or getting pushed up when you plug the 24 pin ATX plug into the board.

I've ran into this before myself and it had me going in circles for awhile as to why the plug was so hard to plug into the board.

As to why - All it takes is for it's pin in the board to not quite be straight like the rest and it won't go into the connector's hole in the plug itself, instead it will push the individual wire in the plug up, causing poor contact and you'll have this problem.
Note the pins in the board must all go into the PSU plug and there are holes they all must go into, these are the individual connectors in the plug and a pin in the board that's off/not going into the hole will make it push it's individual connector inside the plug up, plus that makes it harder to plug the main connector into the board.

I recently got a Gigabyte Aorus RX580 8gb, and it's been running fairly hot at idle, around 60C. Then, I noticed in MSI Afterburner that it's running at 100% GPU usage, despite the fact that I'm not running any games, just chrome. Reviews for the card had said it ran hot and the fans were loud, but I didn't think that it would be like this. Why do you think this is happening?
 

I have a Ryzen 5 1500x on a MSI B350 Pc Mate, using 2 x 4 corsair vengeance lpx at 2400, a hand me down msi gtx 660 oc, 2 stock 120mm fans from the p400s tg case from phanteks, as well as 1 120mm pure wings 2 from bequiet. My cpu cooler is the be quiet pure rock. My psu is the corsair cx650m. My hdd is a 1 tb sshd fire cuda from seagate.

Also, the gpu is old, so I will see if the buzzing persists once I upgrade.

did you remeber to take off that plastic film on the heatsink on the cpu cooler?

Another way to do it, find a prebuild or even a couple online of equal spec to your brother's, then show her the prices.