In my 94 the safety switch is a lil off canter when replacing my old transmission, I just push up the shifter all the way up in park pushing in the button aswell and she starts..... also try in neutral pushing forward or back to see if that helps......
There is also a thread on adding a relay to the system on here somewhere that helps with the clicking and makes the starter turn over quicker, if it isn't the safety switch you can try that.