News:
Have you seen if you are getting juice to the relay? See if it will turn over or even TTY to crank by putting the key in run position and jumping the two large terminals on the relay with a screwdriver . If it does then it's a bad connection between that and your switch.
poor contact on the yellow wire through the firewall maybe
It would be a good start. Remove the middle bulkhead connector, check the blades-clean if needed. With an ohmmeter you could check the continuity of the yellow start wire just to make sure the wire is ok and not broken. If everything seems ok in the engine compartment then maybe it's the connector at the steering column. Take apart the connector (square on both ends) and check the terminals. With the ohmeter again you could check your switch-just cuz it's new doesn't mean it has to be good. Put your leads on the yellow and red wires going into the column while somebody turns the ignition switch. The meter should drop to near zero. Reconnect and try to start. Hopefully one of these steps finds your problem. It's probably a good idea to disconnect your battery while screwing around with the connectors.