Check Device Manager for the make and model of the ethernet card, and find the manufacturer's site for generic driver for your model number/range.
Check HP/Compaq's site to see if there are XP drivers for your laptop. If they have only Win 98 drivers, they may give you the make/model of the LAN card. If not, you could download the Win 98 driver.
HP's installable executables are usually ZIPped files, even if they have a .EXE extension. If that's what you find, you could use WinRAR, or any other unizipping utility that allows you to look inside of the file without running it as an executable installation. In it, you'll probably find a Read Me file that may help you determine the make and model.
You can also search Google for the model + driver to find it.
Of course, there's always the possiblity that there is no XP driver for a machine old enough to have been released with Win 98.
Hope that helps. 🙂