Okay, did some testing (once I dug out the multimeter)
Bare battery 2.949v, voltage on the pins shown by Manul 2.888v
Tested button continuity, worked fine. Tried manually shorting button, no difference.
When button pressed 2.793v shown.
So looks like something is happening as far as the button press is concerned, but no LED, no car response.
Multimeter is a Digitech QM1323 (don't roast me, was all I could get at short notice)