Hi Jordan,
Just to add:
This is most likely caused by 2 things.
1: The power supply. I would replace this one for a new one and see how that goes! It's not that expensive and a great test to begin with. Also easy to replace.
Guide: [guide|103362|PlayStation 4 Slim Power Supply Replacement - iFixit Repair Guide|new_window=true]
2: The APU. This one is very difficult to fix and requires soldering and some serious soldering skills to get it fixed. You can reflow the APU, which is easy but most of the time temporary. Otherwise you need to reball it, and this is very difficult and requires also some expensive tools.
If you need any guides for this, please let me know!