Who makes the motherboard? If it's truly an "Intel" board, then it's probably in a Gateway or similarly-branded make of PC. If you pop the case, see if you can find a name like ASUS, Biostar, ABIT, Gigabyte, PCChips, etc. Then hit their website for chipset drivers.
Additionally, if you can find the VGA chip on the mobo, look for the part number and google it with "xxxxxx drivers" or "xxxxx chipset drivers". You might have some luck finding someone's website that already found and cataloged the drivers for you. I've done this a couple times in the past with reasonably good luck. The ones that didn't pass muster, I just installed a cheap-o video card that got the job done (usually from my spare parts collection, or super-cheap... like $5).
I agree with all the other posts. The monitor is "dumb" and will accept and display whatever is sent to it, as long as it's within it's range of operation (resolution, refresh rate, etc). The VGA chipset drivers are the key.