1992 Olds 88 doesn't start

I have a 1992 olds 88. The car is not starting. There is a ticking/buzzing sound from what looks like a relay under the pass side dash. There is nothing from the motor, no cranking at all. The battery reads 12.3 volts, also at the starter, and I have good battery cables and connections. I have recently replaced the starter for the second time in the last 7 years. I replaced the alternator about three yrs ago. This has been happening over the course of the last couple years. It will just shut of while driving or not start after a drive of about 20 mins or so. Sometimes it will restart after some time, around 20 min. I have looked at the ticking/buzzing relay and replaced it with one next to it and it does the same thing. I have read some threads about some sort of four bolts to tighten regarding the tilt steering and also ecm replacements - I know nothing about troubleshooting either. Any advise? Is there some sort of detail as to what this relay is or what circuit is that I can attempt to troubleshoot, and how to? The Haynes manual has some nice wiring diagrams but I have no idea what this relay belongs to or if its just reacting to another circuit that is having faults.

update - I was about to swap the ecm and was removing the positive battery connection to the battery and noticed some corrosion on the inside of the +pos battery cable that makes contact to the battery post/screw. Cleaned using a round wire brush and the car starts like a gem... Guess I didn't clean it as good as I had previously thought, but wanted to let the forum know the importance of a thorough cleaning of the battery cables / connection to the battery is critical.
Best Regards - jhmcar

There was a thread a while ago about checking for corosion within the molded double cable connector on the + terminal,a good place to start. good luck.

what i do to those type of battery terminals is soak them in a baking soda and water solution for a while and it will break up the corrosion inside of the terminal. rinse well afterwards(thicker corrosion= longer soakin)

Just want to thank AF.com, auto trainy, & back2life for all the feedback. My car is running great since the battery terminals have been immaculately cleaned. This site has been the best resource for automotive help. Keep up the great job in responding to all.