Hi Kris. Does the Console have any notable history of drops or of water damage? Are the vents filled with particularly heavy deposits of dust? Any of these answers may point closer to a solution, but PS4 repair can be pretty open-ended if the cause is unknown.
If you have hours, and I mean many hours of spare time and would like to troubleshoot this yourself, I recommend watching some of the PS4 YouTube videos by Andrew Paul. You will also need to get yourself a set of security torx screwdrivers to even begin any PS4 disassembly.
It definitely is worth testing a new power supply on your console, if only because so few screws are required to swap the PSU and you don't have to take out the motherboard to get to it. The power supply is not *very likely* though. A dead power supply would mean no light and no beep. So in your case, it could be a failing power supply. Maybe you can purchase a new PSU from a seller with a good return policy…
In my experience, consoles like yours usually have a complex motherboard problem. However that's where 50 hours of free Andrew Paul videos come in handy!
If you don't want to deal with this yourself, call around to the local computer repair shops and cell phone repair shops specificly asking if they work on a lot of PS4's. You don't want someone with no experience simply taking a heat gun to the motherboard “because they saw it in a video". That type of troubleshooting can only make a board unrepairable. In most cities, the CPR Cell Phone Repair franchises either fix PlayStation 4 in house, or they escalate the ticket and ship them in to CPR corperate.
Just keep in mind a few things: you can go on OfferUp or Letgo to buy a used PS4 for only $150-200 if repair is too much trouble. If repair is too costly, you may be able to sell your dead PS4 to the shop for $25-$50. If the motherboard really is dead, don't expect a shop to offer you a lot of cash for the box. It may have a lot of $50 parts inside, but they have no way of knowing the history or condition of those parts or if they will actually need them in the future. Take whatever cash you can get if it really isn't fixable.