Toyota Repair: Starting problems, jumper wire, loose ground

Question
I'm trying to help a friend get her car started, with no luck. It is an 86 Camry wagon (gas, auto). The car wouldn't start hot, and started erratically when cold. I took out the starter had it tested, then replaced it when the testing showed it was bad (it was an 87 starter according to autozone, so I'm not sure if it is an 87 camry or if it was just an end of the year production car with an 87 starter), then the car started once and won't even crank now. The battery is new and fully charged, with 12+ volts getting to the starter. How can I test the ignition/starter relay, how can I test the ignition switch (the key can come out in any position). If it is a fusible link, where is that located? I am assuming that it is not the ignitor, because it appears to be a starting problem, not an ignition/spark problem. What other sources exist for this problem, how and where do I test for them? Thank you for your time.  

Answer
Check the battery teminal connectors on the battery and make sure they are clean and tight, eliminate the starter and battery as the possible problem by disconnecting the small electrical connector on the solenoid, the put a jumper wire from the positive side of the battery directly to the small terminal on the starter, make sure the ignition is in the off position, the engine should crank over by doing this.
If it does the problem is either with the ignition switch or the neutral start switch on the transmission, if it still doesn't turn overthere is a bad connection between the positive side of the battery to the starter or a loose ground cable from the battery or loose connections on the battery itself.