Assuming the PSU is known good, it’s likely that there is either a dead short on the motherboard on one of the rails, or there’s a blown fuse.

The motherboard led came on twice intermittently during separate times after adjusting the ATX power connector. The board also started up on shorting the power pins. However when I switched off the PSU and back on without disturbing the ATX connector, there was no light - meaning no power.

I tested the board with a few PSUs and there was still no power to the board (led not on). Had noted 2 fuses beside the power connector and near the PS2 and usb ports. Tested these and it had continuity.

Is there anyway to test the power rails on the motherboard?

You should really get a bios post code analyser card and see what codes You get.
After a long while in storage the cpu and memory sockets might be oxidised, Clean contacts where possible.
I was in the same situation, 3 socket 370 boards that either don't work at all or lock up when operating. I purchased one of those NOS
chinese boards from Aliexpress and it's rock solid stable.

Imperious wrote on Today, 00:15:

You should really get a bios post code analyser card and see what codes You get.
After a long while in storage the cpu and memory sockets might be oxidised, Clean contacts where possible.

The problem is there is no input into the board in the first place. When I connect the ATX plug to the connector and switch on the PSU, the first sign of life is the motherboard light switching on. This itself does not happen.

I also tried switching on the board without this light but there was no booting possibly up due to lack of power delivery anywhere on the board.

I would inspect the board very closely again, checking for damaged traces or loose soldier joints. Try pressing down on the chips/wiggle things, since you said the light flashed a few times. Could be a bad BGA?

If you can get some high-res images of the power area and the back, we could take a peep, too.

Did you ever replace B116?