Do you have this model? http://www.uktsupport.co.uk/pb/mb/450.htm
If so check J19 that enables onboard video
Maybe two beeps suppose you press "F1" key because of some error during the start

Yes this is the model I have
Tried to disable on-board video using jumpers and the only difference is the monitor stays in stand-by and not turns on, and two beeps again.

How about the processor? Is it currently installed or was it removed at one point in time?
Also, check to see if the Parity (J18) is set to pins 2-3 or 1-2 and install a battery on the jumper for the battery since the one that's on there might be dead.

Check for oxidation by spraying contact cleaner in the VGA port as well.

The processor is OK, I also tried replacing the CPU from another board.
I also believe the memory is OK
The reason why I think so is because I was able to flash the bios using built-in recovery routine (using J17)
I think it requires working CPU and memory

That's true. Did you change the jumper for the recovery (boot block) mode back to normal mode afterwards?

If you have the ISA Bus Extender (riser card) and an ISA videocard you can disable built-in video and try discrete one.
The reasons are:
1. maybe onboard video is PCI and because of broken content of bios the pci-part of chipset isn't initialized
2. maybe onboard video is bad

P.S. There are two different bios versions for PB450: for ISA model and for PCI model.
I don't know what it means 😀 Is it about the riser or videocard or chipset? Can you upload high res photos?

Yes I changed J17 back to normal operation of course. I flashed bios for ISA system.
Onboard video is based on CL-GD5428 chip and it is VLB AFAIK
Unfortunately, I have no spare ISA graphics card so I can not verify if it's the graphics card that is faulty.

a few photos attached

Post pics of the motherboard and the whole PC so that way everyone can help you out with the issue. Does the monitor work with another computer?

Added the pic of the motherboard above.
Yes the monitor does work with another computer.
Here is a video of the problem: https://photos.app.goo.gl/J71n0f2BYQI8EYmJ2

Remove the jumper (J33) by the PC Speaker (LDEV bypass) since it looks like it's enabled and see what happens.

Removed J33 and now it does not beep at all
Simply nothing.
Dont know what "LDEV bypass" is and whether it should be enabled by default.

I see you don't have a riser card installed. Was it installed previously? Also, put the jumper back in. The LDEV Bypass is used for ISA slots.

LDEV Bypass
Enabled --> ISA
Disabled --> PCI

And what about J9 (Video IRQ enable) ? Should it enable or not by default? It's different in different sources.

On my motherboard, mine is disabled since the MPU-401 card I have uses IRQ 9, but, it varies.

Sources:

1) http://www.uktsupport.co.uk/pb/mb/450.htm
2) http://www.arvutimuuseum.ee/th99/m/P-R/33546.htm

Enabling it should make the system boot up without issues.

I do have a riser card (ISA), but it's presence or absence does not seem to have any effect.
J33 behavior is the same
Also tried changing J9 and no difference

How's about J20 (I/O)? Is that set to enable (pins 2-3) or disable (pins 1-2)? Maybe the video BIOS went out on there. I can dump the BIOS contents for you in case you need it. Do you have an EEPROM programming tool? If not, I can make the BIOS chip for you.

Tried to disable J20 - no change. Two beeps.
I don't have any EEPROM programming tool, and I'm not able to locate video bios chip on this board.
I suspect it is in the square chip n82c42pe (shown in the first photo above)
I will still probably be able to replace the chip but don't want do mess with it until I'm sure it is the cause of the fault

Is it possible that Video bios is located in the same socketed chip where the main bios is?

That's my guess, too.