Load the Broadcom or Intel PRO/100 VE driver. Without network, you are stuck. You can use a USB stick with another PC to transfer drivers.
If you find driver files, check these MD5s from original HP SoftPaqs (XP 32-bit): hp compaq dx6100 mt drivers
This remains the best OS for the dx6100 MT. With the drivers listed above, it runs Microsoft Office 2003, classic PC games (Diablo II, Age of Empires II, Half-Life), and legacy industrial apps flawlessly. Load the Broadcom or Intel PRO/100 VE driver
The SoundMAX AD1981B driver often requires the “Microsoft KB888111” UAA HD Audio bus patch first if you are using a high-definition audio variant (unlikely on dx6100 – it is pure AC’97). Install the driver directly. If you hear no sound, check that “Audio Device on HD Audio Bus” is not disabled in BIOS. If you find driver files, check these MD5s
Use the HP Support website with the precise product number (usually on a sticker: P8687A or something similar). As of this writing, the FTP archives at ftp.hp.com may still hold some SP (SoftPaq) files. Search for “SP29866” (audio) or “SP30185” (chipset).