240V L1-L2, L2-L3 and L1-L3 with 128V L1-G, L3-G and 0V L2-G . Did you also measure L-N _at the transformer_?? Does the transformer have a neutral?
The older machines are three phase motors, not single phase motors tapped off of 2 legs?
If the transformer has failed and is no longer producing 3 phases, then it couldn't start a 3 phase motor spinning. (Note: an already spinning 3 phase motor that loses a supply phase can keep spinning, and if lightly loaded will function just fine. It can even act as a RPC and generate the missing phase for other loads. This is why I asked if the older equipment was stopped and restarted.)
If you have a solid 3 phase 240V, then getting the 128V measurements requires some sort of neutral, but not at the strict neutral point of the system. A solid 240V single phase neutral would give you 120V (with 208V to the high leg), a solid 3 phase neutral would give you 139V.
I am sticking with my hunch that the transformer is now no longer properly bonded to ground, if it ever was. On top of this I think you have a L-G load connected.
-Jon