I have to believe then it is a bad mb.
At this point you could purchase a new mb that will work with your cpu or buy a mb and new cpu and fan and do a upgrade. Being a HP that may be a costly adventure. I believe HP's are proprietary which means their mb is all that will fit in their system. Please look HERE
and let me know if this looks like your mb. HERE
are the specifications for your system. From this page you can get to the support page and contact information for HP. The other option you have is to purchase what is called a barebones system and rebuild a new system using the parts you can out of the HP. Let me know whiich route you would like to take and I will be here to assist with anything I can.