since the board is dead, soldering a two pin jumper is moot, but your aurgements about how the two missing pins soldered into the boards existing Jumper #29 are not a valid comparision in my opinion
just because the 2metal pins are not soldered into Jumper #29's location does not make that location nonexistant
the two metal pins simply make it easer to connect/short those two traces on the board you could in practice use two probes connected by a wire and acheive the same result, or you could solder a brige wire between the pads both of the above methods acheive the same result as soldering in the pins and placing a jumper on it (IE-connecting the traces)
while i understand you are unhappy about the non working board and the fact that you may have to solder a two pin header on the board also makes you unhappy, it does not and will not change the fact that the location exists and the nessary jumper header can be installed at Jumper location #29
If/when you buy a new board you may wish to have the jumper installed on the new board if it's lacking before installing it.
last, as i have mentioned here before the HP power supply is non standard, and does not follow the ATX pinout connecting a ATX power supply to a z220 may cause damage to the board or power supply. there are however premaded adapters for using a ATX supply in the z240, google for them