|Are you 100% sure the board is bad?|
The problem with "lunchbox" PCs is that the primary components (motherboard & power supply) are proprietary. Standard "off the shelf" parts will NOT fit. Everything you need to know is in the link you provided. This says it all:
"Shuttle FB83, Shuttle form factor, proprietary design for SB83G5M
chipset: Intel 915G + ICH6R"
In other words, you'll need to purchase a replacement board directly from Shuttle.
The Intel 915G / ICH6R is outdated...it's time to buy (or build) a *real* PC.