Hello experts!

I'm hoping that this will sound familiar to someone. I just replaced a new battery with a newer battery, but the car won't start. Here's what happens:

1. Try to start the car three times
2. It turns over, but does not continue to run
3. The 4th and all subsequent times I try, the starter does nothing - and no sounds are audible
4. The console lights up, but nothing happens

Any insight from you experts is greatly appreciated!

Brad