I rebuilt 3 -35 CPU's recently, I had similar issues and was shorted solder across 2 pins on one, and no continuity on other 2 boards. You need to check continuity below sockets (parts side of board) especially where traces go up board and down board. Also the same principle on underside of boards. Also subtitite plug in chips from another working board if you have some, and if you have another set of ROMS from another game (same chip type as existing ones) it should boot to 7 flashes even if it does not play a game this will prove your other chips (other than ROMS) are ok - With reference to stuck on solenoid have you checked the transistors on diode setting and all within correct range?

Brian