Rob,

The first thing I always do with any new machine is (a) remove all fuses and check with DMM and ensure it is correct type before it goes back in.  Next is to visually inspect everywhere - ie behind displays, under playfield, on top of bumper coils etc... for any loose screws which may have come loose and shorted out G.I strings or your switch matrix.

Given that you've disconnected the 'out' / playfield side of transformer and it smoked and popped, me I would get this checked first.  I've never seen a transformer with that much corrosion on it.  ??  Is there any marks on the bottom of the cabinet - ie if someone has spilt something on it perhaps?

Once you know the transformers AOK, then as Ajlaird rightly suggested you will want to check everything upstream.  In a situation with a non working project you don't want to ruin good boards by rushing and missing something obvious causing you more headaches.  Given the cost of the machine, you can expect to have to purchase some things but if you take it slowly and methodical with a copy of the schematics on hand you'll have it up and running in no time!