Help diagnose starting problem

My daughter and son-in-law have a 92 Olds Cutlass Cierra with the 3300
V6 engine, auto trans, and a/c.

The other day they were driving along, and the engine just quit. While
they were still rolling, they put the trans in neutral and tried to
start it. The engine turned over but would not start.

When they came to a stop, they tried again to start it, and it
wouldn't do anything. When they turn the starter switch, nothing
happens. You can't even hear the solenoid clicking or the starter
trying to engage. No sound at all.

The battery is fully charged, and all of the guages, etc., and other
electrical devices are working. I would appreciate any suggestions as
to how to troubleshoot this.

JFM