Your button wiring is weird. You're using the internal pull-up, so just connect one side of the switch to ground and get rid of R1 & R2.
It also seems strange that you never reset buttonpushcounter, although it's probably OK if it counts forever 'till it rolls-over.
The protection diode on the solenoid isn't wired right either ([u]example[/u]).
What's the coil rating on those relays? It's unusual to find a 120VAC relay that can be driven directly by the Arduino. And your relay coils need protection diodes too.
You might add a few more Serial.print messages so you can "see" what the program is doing.