Ok I'll give you a step by step.
1. Be sure the shift lever is in the park position.
2. Attempt to start engine. If engine doesn't start proceed to step 3. If engine starts skip to step 11.
3. Make sure the battery is charged.
4. Check that the connections on both ends of the battery cables are tight and clean.
5. Attempt to start engine. If it doesn't start proceed to step 6. If engine starts skip to step 11.
6. Check for 12v on the "S" terminal on the starter solenoid while someone else turns the ignition key to the start position. FYI the wire in the original harness should be purple. If 12v is present then you have a issue with your starter. If 12v is not present continue to step 7.
7. Check for 12v at the neutral safety switch while the key is turned to the start position. The switch is located on top of the column down next to the firewall. The top two terminals are for reverse lights. The other set breaks the start circuit when the shifter is not in the park or neutral position. In your case originally there would be a purple wire and a yellow wire on the terminals. When the key is turned to the start position there should be 12v on both the yellow and purple wires. If there is voltage on the yellow wire but not the purple then replace the neutral safety switch. If there is not 12v on either terminal the problem is probably the ignition switch. If you have voltage on both terminals proceed to step 8.
8. Check the connector where the purple wire comes through the firewall. With the key in the start position there should be 12v on both sides of the connector on the purple wire. If not unplug connector and check for corrosion and clean if needed. Be sure the connector plugged together fully and that the terminals fully engaged into the connector housing. Proceed to step 9.
9. Attempt to start engine. If engine doesn't start proceed to step 10. If engine starts skip to step 11.
and proceed to step 11.