There is a test for the power transistor. Using a 1.5v source (1 AA batteries should be close enough) you put power on the PT as follows:

looking at the PT connector (on the PT!), the terminals are 1,2,3, with the catch up.

Connect the negative (-) terminal of the 1.5 power
supply to terminal 2 of the power transistor, then check
whether there is continuity between terminal 2 and
terminal 3 when terminal 1 and the positive (+) battery terminal are connected and disconnected.
Terminal 1 and (+) terminal connected, continuity between terminals 2 & 3

No battery connection, no continuity.

I think you have a bad PT given your test results.