I had this problem once on my Suzuki and was able to solve it in 5 minutes.
your problems suggests that you have a blown fuse or some of the wiring may have been chewed off by rats etc or may have got disconnected. replace the fuse or the wiring and your car will hope fully start.
the car will start if pushed, key on, and gentle push on accelerator; but won't crank over. battery is good, indicator lights on dash light up brightly and stay that way even if the key is turned to on or start. there is no audible click from the solenoid. if headlights are put on, they don't even dim when key is turned. car is other wise in good mechanical condition.for several months leading to this, alternator light would dimly to moderately light up while engine was running. a mechanic said the alternator's diodes were not functioning, however, the battery continued to hold a charge for about 5 months before the car no longer would start on its own.currently unable to take to a mechanic and must solve this another way.the starter is a rebuilt unit with approximately 25,000 miles on it;alternator also rebuilt unit with approx. 30,000 miles on it; ignition coil and distributor are original with 234,000 miles-rotor a little worn,but otherwise appears O.K. car had new clutch disc, pressure plate, pilot bearing, and throwout bearing installed with a resurfaced flywheel 5,000 miles ago so I don't want to part with this car and it passes smog testing with ease. please help.