Toyota Camry no engine turnover

Hi, My 1994 camry V6 auto[110 000 miles] has gone from brilliant to dead overnight. When turning the key, I get all dash lights as normal but nothing from the starter- no click from the solenoid, no dimming lights under battery load, silence. I checked the battery, and the 2 fuses marked in the handbook - a 10 amp and a 40 amp main - all ok. Next tried the transmission" only start in park" micro switch, which I can see but dont know how to find out if working - Its 3 wires to a black box marked transmission shift computer, or something - Toyota never made anything simple. I noticed a hesitence to turnover a couple of weeks ago but It came and went - its pointing me to this transmission switch. I dont know where else to look and the car is immobile
Thanks