Yea, that's the video beep.

Did you try the video card in multiple slots?
You can do a rather quick test by measuring in diode test range. Plus of the MM to GND on the mainboard, with Minus you probe each ISA pin. On nearly all data lines there should be a parasitic diode. Power pins don't have them, but you can do a continuity check to the power connector.

Thanks for advice. Yes, i tried every slot but it didn't work. I did the testing and noted voltage drop values (i can compare that with working mainboard, but i'm not sure if it will help).
Here is what i measured. There are no unconnected pins and most of pins have ~650mV voltage drop. But some of them have ~860mV voltage drop, i don't know if that is okay or if its due to corroded traces.

Hmm, the A26/addr05 looks suspicious. It differs from the other address lines. I read it as being connected to something, but not to everything. But it's just a guess.

The differences to ~860mV means that they are connected to different chips/pull up resistors/input or output types. But they roughly match by function, except addr05.

Here you might find the pinout of the 82C206: http://www.datasheetarchive.com/HM82C206-datasheet.html
This chip contains the on-board functions like timer, IRQ controller, DMA controller, memory mapper. It is either directly connected to the ISA bus, or bus drivers are in between (the 74*244, 74*245):

'Northbridge' <--> 82C206, bus driver <--> ISA slots
or
'Northbridge' <--> bus driver <--> 82C206, ISA slots
or maybe another combination. This info might help you to trace down the connections.

Just a quick suggestion: There is a mono / color jumper on the board. Could it be related?

I just fixed a 286 motherboard with AMI BIOS and during the process also got two high-pitched beeps followed by eight lower-pitched beeps.

In my case, connecting a video card was all it took to get a picture. However without the card, the machine still continued to boot after playing the beeps. I could still hear the PC speaker clicking as it was performing the memory check. Do you have a POST card? I was able to use mine to see when it was performing the memory check, asking me to press DEL to enter setup, and displaying an error message all without having the video card present.