Occasionally over the last few months, my starting system has been acting up in one of two different ways. After turning the key on, and the "click" from the solenoid*- one of two things occurs; there's either a one-half to one second delay before the starter engages- or the starter doesn't crank at all.
Usually its been the former (delay). On the few occasions when the starter didn't engage at all, it finally did after 5-10 minutes and a number of attempts. Either way, I always get that immediate "click"*. Is there a relay somewhere to be considered?
Thanks to all for any insight.

*I assume the click is from the solenoid...

 

You are probably correct suspecting the starter solenoid. There are a couple of other possibilities that you might check like the battery cables for hidden corrosion, neutral safety switch connections ,starter solenoid and last the starter itself. It does sound like the starter brushes are either worn or hanging up. There could also be a bad spot on the starter armature where there is no internal contact. If the spirit so moves you, the next time it won't start you can try tapping the starter with a hammer and see if that at least allows it to start. Otherwise it just may be time to replace the starter.

 

I don't think you can get oem cables any more when replacing battery cables. I would try replacing the starter first and see if that don't solve the problem. I don't know if the put two solenoids on those cars ( one on the fender well and one on the starter) or did away the one fender well and put it directly on the starter like they do on most Gm's or mopar