This model already tested with Windows 8 (The edition was Windows 8 pro), and it turn out all of the drivers automatically installed except Card Reader and HP 3D Drive Guard. So here is the drivers you need to install:
Driver 1 : Ricoh Card Reader Driver
Driver 2 : HP 3D Drive Guard
HP 8510p Drivers for Windows 7. (32 and 64-bit)
HP website provides the original drivers for this model on their wesite. If you want to download it right away here is the quick direct link:
Audio : ADI AD1981HD Audio Driver for Microsoft Windows 7
AMT Chipset : Intel AMT Driver
Storage : Intel Matrix Storage Manager
There are 2 applicable Graphic driver for this model, choose base on your specification.
Graphic : AMD Graphic Driver
Graphic : Intel Graphic Driver
HP QL : HP Quick Launch Button
Touchpad : Synaptic Touchpad Driver
Modem : Conexant High Definition Audio Modem
Wireless : Broadcom Wireless Driver
Wireless : Intel Wireless Driver
Bluetooth: HP Integrated Module with Wireless Technology
Card Reader : Ricoh Media Card Reader Driver
Security : HP 3D DriveGuard