Just brainstorming here... if the problem has not been resolved by any specific BIOS settings changes.
Have you tried clearing the NVRAM? It is possible that some funky or corrupted state data may have gotten stuck in there. I have successfully repaired a few notebooks (and desktops) in the past by clearning the NVRAM. All of which exhibited some form of strange and inconsistent boot and power management related problems.
<WARNING>If you are not comfortable opening up your notebook and working on the guts, then stop right here. If the notebook is still under warranty, then stop right here. This procedure requires you to work inside the notebook, which could result in permanent damage to the hardware if done incorrectly. If you are not comfortable, I would seek professional assistance from an authorized repair center. This one is fairly simple as it is done from the memory module cover on the bottom, so you don't need to get your hands too dirty. I hereby release all liability if you brick your notebook.
If you are comfortable, and accept the possibility that you could permanently damage the system, then you will need to download the service manual for your notebook series
http://h10032.www1.hp.com/ctg/Manual/c01035677.pdfMake sure you are in a clean and static free environment.
Refer to section '5.7 RTC Battery' and follow all of the instructions for preparing the notebook for disassembly.
Basically, you just want to disconnect the battery cable. Then you want to short the two pins on the battery connector on the motherboard. Use a paperclip or the tip of a non-magnetic screwdriver. DO NOT SHORT THE PINS ON THE BATTERY ITSELF!!!
Then, reconnect the battery cable and complete the reassembly.
On first boot, you will need to go into BIOS and reload the setup defaults, as well as the system time, and any other customizations you have made (ie boot order, etc).
If you are uncomfortable with any of that procedure, then please do not attempt. In any case, we would like to know the outcome of your efforts.