I did find out the extra zero in my search, thank you. Now I got a few hits at digikey. No, I don't have a FLASH programmer, but i can purchase one if needed, and the price is not to high. According what you write it
Depends on the model.. You can spend anywhere from $200 to $2000. There is a USB one from batronix that is fairly cheap but I can't recommend it since the software sucks and its never worked correctly for me. Others on the list have not had issues with it though.
Google for "flash programmer" or "eprom programmer" and see if you can find one in your price range. Also unless your chip is a DIP you will have to buy an adapter which will be around $100.
One quick check. Your flash chip is socketed right?
does not seem to be possible to program an empy BIOS with a boot floppy similar to re-programming an existing one. Can I copy the content of the old BIOS with a programmer and start from there? How to proceed?
Right. You cannot program a blank BIOS chip with a floppy. Since the board needs the bios to boot. Most setups have a recovery image that you select with a jumper or something that will boot the machine up enough to load from a floppy. This recovery image or "Boot block" is protected so it cannot be erased. So you never really fully erase your flash.
If you have a programmer then you can extract your bios image from the existing part (or get a copy from the web) and program whatever you want back in the chip. Or get any 2Mbit chip supported by your programmer and use that. Flash parts program differently but they all read exactly the same.