Current laptops have SATA hard drives. Back when Win XP was released there was E-IDE hard drives. The SATA interface did not come into existence until around 2005 or 2006. Therefore, Win XP does not natively support SATA drives and that means it will not recognize the hard drive which is most likely the reason why you are getting the ASPI error.
During the installation of Win XP it asks you if you want to install additional driver. It is at this point you would typically insert a floppy disc that has the necessary drivers for the SATA hard drive. Naturally floppy drives are not standard on laptops... or desktop computers. If you have a flash drive, then I believe you can also install the SATA drivers from it, but I have never done it before.
I would say that you need to find Win XP compatible SATA drivers for your hard drive brand. Additionally, many of the devices in the laptop would also need the proper drivers to operate correctly if you install Win XP. Therefore, you will need to search drivers for such things as the wired and wireless modem, camera (if there is one).
Additionally, many laptops come with switchable graphics. That means the laptop's CPU has a integrated graphics core (like the Intel HD 3000 in the Sandy Bridge Core i3/i5/i7 series, or the Radeon HD 6xxx core in AMD's Llano APUs), and there is also a dedicated graphics card like a nVidia GT 550m or Mobility Radeon HD 6670m. These types of laptops requires specific graphic drivers from the manufacturer (in your case HP); you cannot simply download drivers from AMD or nVidia they simply will not work. Which means HP must develop and release Win XP compatible drivers for switchable graphics. I can guarantee that will never happen since it is an old operating system that has basically been replaced by Win Vista and now Win 7.