Turn off the computer, then unplug the battery (leave the power cord connected), then wait a few minutes, and plug the battery back in. If the charging indicator on the laptop lights up for a second then turns off, or does not come on at all, continue. If the charging indicator stays lit, leave it overnight (about 8 hours should be enough for even a stubborn battery) or until the light turns off, then continue.
Unplug the power cord and try to boot it up. If it does not boot, skip to the next step. If it boots and stays running a while, then run it until it dies (might help to set the Warning and Critical battery levels in Windows as low as possible, and run it in High Performance and disable Sleep, etc), then try charging it again. If you can charge it now, you're done, your battery just needed some sense kicked into it (some people call this recalibrating the battery, although I'm not sure if it is the right term). Leave it plugged in until the charging light turns off and do not unplug it or boot it until then. If the light does not turn off after 8 hours, the battery does not appear to charge at all, or the light has turned off, continue to the next step.
Plug in the power cord and boot it up, then unplug the power cord. If it turns off right away, order a new battery (call HP support first to see if they'll replace it free or at reduced price). If it continues running, go to the next step.
With the computer running on battery, check the battery in Windows. If it shows unknown battery status or no battery, skip to the next step. If it shows the battery status correctly, plug in the power cord. If it shows charging, you're done. If it says unknown status or not charging with a percentage not shown or less than 80%, continue to the next step.
With the computer running on battery, check the battery in Knoppix. If it shows unknown battery status or no battery, skip to the next step. If it shows the battery status correctly, plug in the power cord. If it shows charging, the problem is in Windows, and you should remove the battery, AC adapter, and anything with ACPI in the name from the device manager then reboot, check for updates at support.hp.com, or reinstall Windows if nothing else works. If it says unknown status or not charging with a percentage not shown or less than 80%, then the problem is hardware related but probably not the battery. Continue to the next step.
At this point, if the computer runs on battery but neither operating system shows the status correctly, look up your computer on support.hp.com and see if there are any BIOS or firmware updates. It's risky, so if you find one, follow the instructions EXACTLY and do not turn off or unplug the computer at any time during the update process. If you do not find an update, the update doesn't work, or you don't feel comfortable doing the update, call HP for a repair.