Delete all the HP drivers before re-installing them. Ignore the windows wizard installer while you install all the HP stuff first. Then restart the system before setting the HP as default. After setting as default restart again.
Then try print and fax.
You may find that you need to install windows .NET framework, up to service pack 2 before installing an HP printer fax. You should probably check that you have it or download it from Microsoft before you install the HP software.
And HP software is a bit more difficult than the average printer, that's for sure.