I have no idea what the problem is because you're not clear about what you
have done.
To install a printer...... download the correct driver from the printer
manufacturer's website... install the software and do NOT connect the
printer until the software tells you to do so. Now you should be able to
print.
You say you installed the printer driver 'on another notebook'. Is this
other notebook networked and you want the networked notebook to print to the
HP Printer you have installed locally on a desktop or notebook? If so, did
you share out the printer?
Tell us what you have already done and what you want to accomplish and we'll
try to assist as best we can, but right now there are so many possibilities
that it would take me a week to work it out.
