Since you have a meter, is it practical to measure the voltage right at the crimped pins in the connector that plugs into the PS2 circuit boards?
I figure this is the last hope for a simple repair - that is, perhaps some broken wire or whatever in the harness between the actual battery and the circuit board. Confirm the 2 gold colored pins in the white battery connector housing are intact (not bent over, pushed downward thru the board, whatever).
If the known-good battery is making its way to the 2-pin white connector, then unfortunately I'd say you have a problem with the battery management circuit. This is something you really can't fix yourself. You could visually inspect the components around the white connector looking for a charred, bulging, cracked, etc. component which would be telling but not helpful in that it's not a DIY repair.
I'm not an authorized MTH tech but I believe the practice in days past would be to replace the so-called PS2 power supply circuit board (the board shown with the 2-pin battery connector). But this board which I believe is no-longer-available was something like $75 (?) and you had to be an MTH tech to get it...then add labor, two-way shipping of the engine, etc.
There are several authorized MTH techs who will hopefully provide more informed advice for this particular situation.
