Battery Install
Check and make sure the new battery has a charge with a meter. If voltage reading is below 12V, then charge it up. Then use the meter to check for voltage at the starter's battery cable post. If you have voltage at the starter post, then it's a matter of the solenoid not closing the switch for voltage to go to the starter. If you know which smaller terminal on the solenoid is the (+), then attach a remote starter switch to it and to the positvie battery cable post on the solenoid. This should engage the solenoid when you press the trigger on the remote starter switch. If the starter engages, then the starter and solenoid is good. The problem is in the positive feed to the smaller (+) post on the solenoid. Tracing that wire back on a diagram will lead you to the problem. Use your digital volt ohm meter (DVOM) and probe that circuit back until you find voltage. What ever is just before the point where you picked up voltage is what is not letting voltage out to the solenoid.