Hi jmancha,
Welcome to the HP Forums! So the battery is fully charged but the laptop will not charge. I will bel happy to help. I would start by trying a Hard Reset. Then reset the Microsoft ACPI-Compliant Control Method Battery which is basically the driver that communicates between the computer and the battery. There is a chance that it is corrupted.
Step 1. Go to Device Manager
Step 2. Select Batteries
Step 3. Right click the "Microsoft ACPI-Compliant Control Method Battery" that is listed there
Step 4. Click Uninstall
Step 5. At the prompt put a check in the box to remove the current driver
Step 6. Shutdown the computer
Step 7: Remove the battery for minute and then put it back in
When the computer comes back up it should automatically find the driver.
Step 8. Go to Device Manager
Step 9. Select Batteries
Step 10. Right click the "Microsoft ACPI-Compliant Control Method Battery" that is listed there
Step 11. Click "Search automatically for updated driver software"
Do the same thing with Microsoft ACPI-Compliant Embedded Controller.
Thank you,