Hi, you have to check the usual suspects:
1) Processor-heat sink coupling(any beep?)
2) Capacitors(bulging/leaking) - pictures will definitely help.

you have already checked the RAM & corsair PSU should be OK. Other than that it is difficult to identify if there is a problem in the motherboard.

I have been told that the Corsair VS350 uses CapXon capacitors and that those are really bad. So it could be your PSU.

Thanks for the help - The processor doesn't beep or make any sounds. But I will check the caps of the board and
try with another psu later, sad to hear Capxon is involved. If that doesn't help I'll take a few pictures of the
board and let you have a look. I also have another mobo, which seems to be Microstar 6116. But I don't know if
it's alive, though I wish it would be, since it has so many expansion slots (3 ISA, 4 PCI, 1 AGP). I could post
pictures of it too.

The manuals for the 2 motherboards you have mentioned are attached(however pcb version needs to be verified).

Your ECS one seems to be the latest one in comparison with your MSI(both 440BX chipset based).

I myself presently have MSI & ECS P3 mainboards albeit with different chipsets. ECS was mine (bought in 2001 start) and the MSI was my relative's (bought in end 2001) and given to me in 2011 as non-working. After 4 years, ECS one started giving trouble. I had to slightly tilt the power connector up at one end(i.e connect loose) for that to boot. That too didn't work after some time. The MSI one had the hard disk dead, replaced it with mine and got it working. After gaining some hardware experience, i fiddled with the ECS one by measuring the resistances in the motherboard's power connector and comparing it with working motherboard. Finally i was able to get it working after i ran a thin copper wire for shorting two of the pins in the motherboard connector. Then the MSI one gave up, stuck in 'Verifying DMI Pool'. Another journey which ended well after recapping. I should say the delight i felt to get these old hardware back in their legs was heaven-like.

Wishing you good luck in your journey, if you choose to start it.

Many thanks for the scans of the manuals, they'll come in handy.

I checked all the caps on the boards, but none of them were visibly leaking or bulbous in shape.
The Corsair psu seems to be dead though, I saw some white yogurt-esque goo spilt over things inside.
That's what I get for brand loyalty. I'll see if I can return it and get the money back, no way I'll want
another one now.

But I got further with the ECS board, with another psu. All the fans were spinning and I even tried
a 40gb hdd to see what it thinks of it, and it held the sounds it's supposed to. But again I didn't hear any
speaker beeps, though actually I've never heard that particular spare speaker beeping anywhere, ever.
Also some red "suspend to ram" light on the upper right corner was burning.

On the back there's a male DE-9 port for monitor, but I'm pretty sure I don't have an adapter now.
I tried with one of my functioning AGP Geforce cards, but got no signal out. Is that normal on older
mobos if there are absolutely no drivers or anything installed? But the fan was spinning and all.

Right now I just need some good indicator of where I am, I'll try another unbiased speaker with confirmed
functionality and get a cable or adapter for that built-in port.

Was this a working motherboard in use earlier or you just got it? Which LED, the one near the panel connector or the RAM? No separate drivers are required to be loaded as the video bios onboard the graphics card takes care of the basic functionality required for a basic display during boot.

I bought the ECS board and got it cheap, but the seller claimed it functions. The MSI board I've had
longer, but there's no guarantees of it. It has been lying in an anti-static bag inside a box for years.
Oh and the led which is lit, is the one by the ram. If it's a problem in ram, I could try with other
compatible sticks. I have some PC133, but there's a "force PC100" jumper position.

Can you post a picture of the motherboard in 'ON' condition? How much experience do you have in assembling?

Edit : I don't think the male port you are referring to is an external monitor port as the ECS motherboard lacks onboard graphics. You have to have an external graphics card

I'll post a picture of it tomorrow. I've assembled about six computers, recently I have put together a mATX build.
But I don't have much experience or knowledge about older parts, or their features.

I don't know, the I/O plate has a symbol of a monitor next to a port like that. But it might not have originally come
with this board.