It's not a machine I'm familiar with but printer/scanners are still
problems by the look of things.
Have you downloaded the HP software for your machine. It seems there
are several F300 series. Here's a link to the F310 page for downloads:
If you have tried to install something else then remove it by
uninstalling not deleting; delete any printer icons in Control Panel /
Printers and reboot with the printer and its cable disconnected from
each other and from the PC. Make sure the printer is not plugged into
its power source, not just turned OFF if it has an ON/OFF button.
Then reboot the PC.
Find the downloaded file and right mouse click on it and select Run As
When the installation procedure tells you to or if it does not after
Finish, plug in the printer and cable and turn the printer on and VISTA
should detect and install it.
If it does not then I guess you'll have to ask HP.
Hope that helps.