Well, right up front, let me tell that the outlook is not good. 10:1 (at least) that your motherboard is bad and needs to be replaced.
The standard troubleshooting approach to this problem is to remove components from the motherboard until you find the one that causes the boot failure.
For these symptoms, I would start by removing all the components - PCI cards, RAM, and even the CPU. The only things you should leave plugged into the motherboard is the power cable from the PSU and the onboard speaker (if that's not an integrated component). You can also leave a fan or two plugged in if you want to verify and visually determine when the PSU is supplying power. With no CPU and no RAM in the board, when you power it on, a healthy motherboard will beep the corresponding beep code, and should also light up the corresponding LED error code to indicate those failure conditions. If (when) it doesn't, that tells you that the motherboard has a hardware fault and needs replaced.
(If you do get the expected beep and LED codes, of course, that indicates that the motherboard is functional and one of the components is faulting and preventing the computer from booting. Add components back in until you add one in that stops the server from booting, and that's your faulty component.)
I've seen this roughly a few dozen times over my career, and I can only recall once when it wasn't the motherboard (the PSU had faulted and was only providing a few watts worth of power - enough for a fan, but not enough for anything else).