efxr6wagon

I'm a rank newbie on this forum, so forgive me if this has already been answered.

My 96 Cavalier 2.4 automatic suddenly refuses to start, or even crank. The "battery" light came on and stayed on, but it continued to start just fine 3 or 4 times. Now when I turn the key, the fuel pump whines, but the starter solenoid doesn't click and the starter does nothing.

All accessories work fine, including the power windows. The battery shows 11.8v, as does the solenoid. I have checked and tightened all ground cables and battery cables. Both solenoid terminals show continuity. I have traced the ignition circuit from the ignition switch, through the transmission range sensor output, and it all gets full voltage with the key in the start position. But the starter motor positive terminal (connects through the solenoid) gets no juice.

I'm thinking it has to be a failed solenoid, as it's getting good battery voltage, but doesn't so much as click. But the thing that's worrying me is that the battery light came on several starts before, yet continued to start normally. What am I missing?

Thanks for your help.