The good news is that HP can run Windows 98. The bad news is you'll have some constraints to get full functionality.
- Memory: Your HP looks like it can handle a maximum of 2GB of RAM. Windows 98 (without modification) can handle up to 1.5GB of memory minus the amount of Video RAM. If you limit your upgrade to 1GB of RAM, you won't need to patch anything and you'll give Windows 98 all it will need.
- Graphics: You can use the integrated graphics if you download and install Bearwindow's VBE VESA mode drivers. The VBE drivers don't provide any 2D or 3D acceleration, but they can handle high resolutions and color modes. If you want to game on this computer, you would need a dedicated graphics card (either a GeForce 6-series or Radeon x-series (x800, x600, x300 etc).
- HDD and CDROM: If your BIOS can configure the SATA ports as "IDE Compatible" or "Legacy IDE", then Windows 98 can use the built-in IDE drivers. If the BIOS has no option, then you could try Rloew's SATA driver. If the BIOS gives you the option to configure the ports in "AHCI" mode, then you could try Rloew's AHCI driver. If all else fails, Windows 98 will access the hard drive in INT13 mode without drivers (not good for performance). You could also use a DOS GCDROM.SYS driver or something similar to access CDs using real-mode within Windows (again, not ideal).
EDIT: You might need to enter the HP's undocumented Advanced BIOS Options (Ctrl-F10, then Ctrl-F11) to change the SATA mode.
- Network: It looks like Windows 98 drivers exist for the integrated Intel 82566DM network port. Search for the Intel Q965 network drivers.
- Audio: I doubt you'll find HD Audio drivers for the built-in audio. You might be able to find a low-profile PCI audio card with Windows 98 drivers, but I don't know any off the top of my head. You could use a USB stereo adapter with Windows 98 drivers instead, but you'll take a bit of a performance hit.
EDIT: Dell used a low-profile Creative Labs card in some of their computers. You could do a search for "Dell 3196W" or "CT5807" to find one (about $10 US). It's a Sound Blaster PCI (a variant of the Ensoniq ES1373). Creative Labs developed Windows 98 drivers for the Sound Blaster PCI. Not the greatest or most feature-rich card, but Sound Blaster PCI cards work pretty well.
- USB: Speaking of USB, your HP's USB ports should work with the Windows 98 drivers out of the box or you could use the NUSB drivers.
- Chipset: Windows 98 should detect and ID most of your system devices with the built-in drivers (the PCI bus being the most important). You could try to install the latest Intel chipset drivers as well. Windows 98 could use them to identify most of the other system devices. Windows 98 would likely work even if you don't have every last device on the motherboard ID'd. If Windows 98 does not install the drivers for the PCI bus during set up, you'll need to run the "Add Hardware" wizard in the Control Panel to add the PCI bus as a system device (Windows 98 will then begin finding the PCI devices).
Good luck.