Depending on what HP supports on this model, you are probably looking at using a USB connected sound "card". If HP does not have Vista and/or Windows 7 drivers and only has XP drivers they are not compatible or fully compatible. RealTek does not deal with consumers, they only deal with OEM manufacturers such as HP, Dell, Acer, or motherboard vendors such as Gigabyte, ASRock, ASUS, etc.
In most cases, Vendor supplied sound drivers are needed for proper operation, as non-Vendor drivers (in this case HP) usually do not work or do not work correctly. Many vendors do a custom implementation of the chip and thus the reequirement for vendor specific drivers for proper operation.