No, You can hear the starter gear engage the flywheel, but it won't turn the engine.
It makes a single loud 'click' when the key is turned- not the ratchety clicking sound caused by a low battery.
Check the ground wire between the engine/battery, battery/frame.
Had that happen on an grand prix years ago.
God I hated that car.
I'm pretty sure its not the ground. I cleaned the terminal off good and its so tight that I don't think its getting any tighter (or loosening for that matter) without breaking the bolt.
The other day, we were able to jump start it using our truck, today, I tried jumping it again, which did not work- and I had the negative jumper grounded to an engine mount. So I'm pretty sure that the negative cable or grounding is ok, or at least isn't the likely culprit.
I actually hated this car and absolutely wished that everyone at GM would die of some sort an AIDS related cancer when the intake manifold melted at around 75,000 miles- which it turns out was happening to just about every GM V6 engine made for about 5-6 years after 1997- those that didn't hydrolock at 70mph when coolant dumped into the intake manifold could be repaired at a dealership for around $1200. Unfortunately my wish didn't come true when Bush/Obama et al bailed those effers out. Its been trouble free for more than 150,000 miles since that event.