Normally you'd first, check the manufacturer's website if they have XP audio drivers. I just checked and I couldn't find sound drivers for XP. They had them for widnows 7 though. What OS did the laptop originally come with? (why not install the original OS?)
There are software that help to detect and install drivers. DriverMax, SlimDrivers, and DriverPack Solution all help to do this. Otherwise, speccy by Puriform gives hardware detail and may help you locate the hardware on your laptop (from there to find drivers).
Websites:
http://www.drivermax.com/
https://www.slimwareutilities.com/slimdrivers.php
http://drp.su/
Other options include an external sound cards that you could plug headphones. Otherwise, a notebook soundbar (goes atop of the screen) and is USB powered. You could also try a linux distribution as they normally have kernel support for hardware, especially since the laptop is older. It requires a bit more of a learning curve though and doesn't natively run widnows software.