Some background, which may or may not be pertinent:

Periodically (a couple times a year) I've had times when I'd receive
an error message on my thermostat, indicate a problem with
insufficient 24 voltage to it. This happened yesterday, after a pretty
bad rain and thunder (lightning) storm. I'm thinking it's related to
wetness, as it has always cleared on its own after a bit. Yesterday,
it did the same working again after an hour or so.

I've had to replace the contactor on an almost annual basis. Not sure
why this is, why my a/c is apparently cycling too often, but that's
for another time.

Today (while dealing with an unrelated(?) problem with my electrical
water heater (still figuring that out), I noticed that there was NO
power to my thermostat. As opposed to an error message, there was no
power. I twisted the R & Y wires together, but still no a/c.

I was thinking it could be the 24 volt transformer, and it's simply
been going bad for awhile? Would it be the transformer that's attached
to the circuit board, and has a black wire going to the contactor?

I manually pushed in the contactor and the condensor turned on, as
long as I held it in. BUT, after about 1:30 to 2 minutes of holding it
in, it shut off while I was still pressing the contactor firmly in.
Still not a good connection?

Any thoughts?! Thanks.