you could always try doing a search on the bios code or anything else it displays on the screen while POSTing
Another possibility is there may be some kind of code on the back. Every electronic device in NA has one, I forget what it is called right now but European equipment might have something similar.
I think what you are looking for is the FCC ID, printed on most, but not all electronic equipment, the FCC ID is usually printed on a sticker carrying the FCC logo, and is a two part code, 3 numbers followed by 1 - 14 numbers, XXX-XXXXXXXXXXXXXX. There are FCC search sites for identifying products using the FCC ID number.
The motherboard may also have identification numbers, or codes, but these are usually pretty difficult to find, however i've had some success in the past when looking up older system motherboards using some of the codes i've found.
The BIOS code is another method of finding the motherboard, however depending on the age of the motherboard this may not easy either, since prior to 80386 systems a lot of manufacturers used their own bios IC's, and these were not always recorded.
From the photo it looks like the bios is certainly pre 386, as it's a pair of eeprom devices with hand written labels, probably a 286, so i'd guess at the 5" fdd being 360K and the 3.5" fdd being a 720K single sided, but possibly a 1.44K as those may have been available, orpossibly a replacement if supported by the drive control card.
Looks like fun to play with, but it's not gonna run PS
