Olds intrigue will not start

I have recently changed the starte and battery in my 1998 olds intrigue. All dummy lights and guages come on, all electrical things work, but starter will not click. The car will start on occasion. what is the deal?

When the work was done, were the battery connectors cleaned and attached wrench tight? Particularly at the starter solenoid?

Rebuilt starter or new?

Was there sparking from either cable that may have shorted something out?

Have there been starting issues in the past not related to the starter or battery? Ignition system fault perhaps?

No there were no sparks and everything is clean on the battery and other connections. I maintain my cars pretty well. I had changed the starter about 2 months ago and the new one I had installed, for some reason stopped working. so I removed it and replaced it. The car started fine, but the next morning nothing. I have read about security issues with this type of car. I did notice that the security light was blinking while the key was in the on position while it wasn’t starting. I disconnected the battery and reconnected it. Then I tried to start it , but no luck. Then I turned the key on and the security light was flashing, I turned the cruise button off and the traction control off and turned the key off and then back on. Then all at once it started and I have not had a problem since. This problem did occur once about a month ago. But , I have no clue what fixed it for the time being. It sounds like a passlock issue, but from what I have read there is no solution. I think I will replace the keys first.

Strange performance alright.

This is just a wild a** guess (WAG) but I’m wondering now if there was/is a stuck relay as well as a security protection fault.

Replacing the keys will be expensive as they are chipped. (a chip in the key head, programmed to the passlock system)

You can have regular keys cut, but they will only be good for opening the doors. (But you likely knew that eh?)