We're still not getting what we need to identify the board, i.e. that string of numbers along the lines of
31571.DO.0000.D.0009061530
Taking another angle on it, looking at emachines parts website says the motherboard for the T1100 is
Anaheim-3 810 Rev. F - motherboard
and there's a bad picture:

There's a better picture at this useful site:
http://www.e4all.info/Click on Anaheim-3 on the menu - they say there are several versions of the board, so you do need to get an ID before flashing a BIOS.
Must do some work now, I'll check in later.