A lot of VGA cards are quite standard, so if you can find one with a socketed BIOS ROM then you can always try putting that "for […]
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A lot of VGA cards are quite standard, so if you can find one with a socketed BIOS ROM then you can always try putting that "foreign" ROM chip into the VLB card's socket. This means you'll boot the VLB card using the BIOS from a different vendor, which may or may not work, depending on whether the BIOS does any manufacturer-specific tricks. I'd be willing to bet that it would work most of the time.
It may not solve your problem however. From your description of the differing beep lengths, what I think is happening is this. With no card detected, the system BIOS can't find the video ROM so does the 1L/3S beep code. With the VLB card installed, the system BIOS runs the video BIOS, which can't then detect the monitor (or has some other problem) and the *video BIOS* produces the 1L/3M beep code.
So from this I would guess that the BIOS ROM is probably OK, and the VLB card's POST routine is detecting some problem, likely "monitor not connected". Given that plugging in even a broken monitor normally stops that particular error beep, I suspect something wrong with the VGA connector on the VLB card.
It could of course be something else (bad RAM etc.) but in my own experience cards from that era typically give you some sort of a corrupted display even if there are major problems.
I will also add that although some LCD monitors are not compatible with VGA cards and won't display a picture reliably, the presence of those monitors is still always detected so the fact that you get a beep code means it's unlikely to be a compatibility problem with the monitor (assuming the VGA cable is not broken/loose or anything.) If it was a compatibility problem you would get no beep codes, and then no picture.