If you can get in there... If you take a screwdriver and use it to connect the big lug on the starter solenoid (where the battery cable connects) to the inside small lug (closest to the bolock) the starter will engage and the car will turn over.
I'd recommend you tape off all but the last inch of the screwdriver. Note that when you make the connection, it will make a large spark. This, accompanied by the engine suddenly cranking over, tends to cause guys to freak somewhat.
Alternatively, you can but a remote start switch for about $10, and hook it to the same 2 terminals. Less change of shorting things out or freaking.
Test will prove the battery and starter work.
Problem could also be the ignition switch or the neutral safety switch. One thing to try (WITH FOOT FIRMLY ON BRAKES!!) is to put the gearshift in neutral, twist the key, and move the shifter a bit toward reverse, then drive, see if you can find the "sweetspot" in the switch if it's misadjusted.