New starter as in new out of the box or new to you but used?
Did you change the bushing too?
Did the starter slip into the hole easily or did you have to pull it in the last little bit with the bolts?
Did you ever determine if your battery is any good?
Checked the ground strap between the trans and body? I mean physically removed it and made sure the ends are clean?
If it's clicking that means it's trying but if it's bound up in the bushing or not getting enough amperage it won't work.
Try jumping between the big terminal with the cable from the battery on it and the little spade type push on one. Don't touch anything else or the big sparks happen. Make SURE the car is in neutral and blocked. If it works then begin to wonder about your ignition switch.