Hi:
There are two problems you have...
1. Your notebook is not supported by HP for W10 and no W10 drivers were ever developed for it.
2. Since your notebook is over 10 years old, HP retired support for your model, which is why you can't find any drivers for it at all.
Below is the link to the Windows 7 Validity fingerprint sensor driver for your notebook.
Info:
ftp://ftp.hp.com/pub/softpaq/sp45001-45500/sp45217.html
Exe:
ftp://ftp.hp.com/pub/softpaq/sp45001-45500/sp45217.exe
If the driver does not install automatically on W10, try manually installing the driver.