Joe,
First of all, yes the power supply can be used. The picture is odd. It appears to have a dual output on the transformer as indicated 18v (yellow pair) 36v (white pair). You want the 36V, higher (up to 48v would have been better IMO but these are minor differences, I would have also chosen a dual voltage in either 48 & 5v or 48 & 12v).
Anyway if you follow that white pair on the transformer, they go to a rectifier or regulator module. It should be clearly marked + and - on the output side. The voltage in the transformer is AC until it goes thru this module. Those 2 will be the voltage supply for the G540.
Regarding the steppers. The pictures are odd. Is it only a 4 wire? Can you show how and where it was hooked up originally? Your prewired DB9 came with a 3.5k resistor soldered in?
Wires 6 & 7 (green and white according to your diagram) are B phase.
8 & 9 (red and black) are A phase.
If you have a meter, you can test which pairs are common to each coil on your stepper. Otherwise the Chinese unknown stepper are difficult to guess. No harm will be done either way on the stepper. It will either work or not. It might go the wrong direction but that can be changed in the settings.
Btw use wire nuts to hook them up temporarily til operational.
This article might give you a little more insight.
http://digital.ni.com/public.nsf/allkb/0AEE7B9AD4B3E04186256ACE005D833B