HP Laptop dies when I remove the ac adapter.

How do you know the battery charges and is fine? Seems like the battery isn't holding its charge. Or the charger isn't doing its job.
 


The battery reads 100% when running the laptop with the adapter plugged in. I also had an older battery that showed 12% and after leaving it in awhile it rose to 29%. My main battery is good.

 
All 100% means is that the battery has charged as much as it can. To a full +12V. A battery that has weak or dying cells may fully charge itself to +12V or more, but it won't hold the charge. Or it will only charge the part of itself that still works, in effect leaving you with a tiny battery too little for the system to run very long on. I suspect the battery first, the charger last.
 
The battery may well accept a charge, and indicate 100% as long as power is applied, but be incapable of holding that charge under load. Either try another battery in the laptop or try the suspected bad battery in another laptop.