you likely need a way to disable the internal video card, which might not be possible. An alternative solution is a rgb2hdmi adapter (if you dont need vga)

The matter is the internal video card is a EGA one and I can't simply connect my monitor to it. I would like to use a VGA card. I tried different combinations of dip switches but didn't gain any success. One thing that I was able to figure out is that switch ten disables/enables output to external monitor of builtin video card.

Yeah I totally understand your problem and it’s not normal to have the option to disable a laptops video card. At least not this early.
The jumpers likely can effect the video out mode like mda/cga/ega.
Take a look into the rgb2hdmi project it can let you convert ega to hdmi.
Mce2vga is another adapter option

Is the EGA BIOS socketed ?

Would removing the EGA BIOS chip or possibly disabling (setting CS or CE line appropriately) the video BIOS chip or even EGA controller chip be options?

No idea whether that's safe/sane or even possible.

EDIT: In addition to the conflict with onboard video, the main BIOS might not be designed to init a VGA card, though maybe that can be worked around.

On that workaround front, if the onboard graphics controller can be switched to MDA or Hercules mode using DIP switches AND if that prevents the EGA BIOS from loading and using the address space VGA needs, it might be sufficient to allow VGA to coexist with it.
Again, please correct any of my potential misconceptions, if applicable.

Unfortunately video BIOS is not socketed and I can not just remove it. May be I try to desolder it and solder a socket and place in it.
Indeed I possess not the whole laptop but just its bottom part with mainboard, power supply and keyboard. So connecting it to a monitor is a crucial task for me.
I found pictures in the net with a post screen, it tells screen type is EGA/VGA.