I have no HP folders in my Applications Folder, as I did years ago. I'm on 10.9 (Mavericks) now.
The Mac OS goes out to the internet to get the driver software that is needed.
If you have installed drivers from any HP disks, unplug the printer cable and Uninstall everything from the same CD.
Go back to System Preferneces > Printers & Faxes.
* Make sure you have no more HP printers or other HP devices.
Note: With Mac OS 10.9, if you hold the Option Key and click on a printer, you will get the option to "Reset Printing".
This appears differen than the previous Apple Technical articles that cover 10.7 and 10.8.
Run the Disk Repair utitlity. (Applications > Utilities > Disk Utility )
Choose your hard disk.
Run "Verify Disk Permisisons" first to get an idea of what's not right.
Run "Repair Disk Permissions"
Reboot.
Go back to "Printers & Faxes" and create a new printer.
The new printer should have an icon that looks similar to the printer.
When you click on the printer icon, a box at the top of the window allows you to choose "Print" | "Scan" mode.
If you continue to have problems, you may need to find some third party utiltiy (like Tech Tools) to completly remove all the HP software.