How did you uninstall the printer driver? Did you do it via Device Manager? If not, try uninstalling the driver via DM then rebooting and reinstalling.
Otherwise - I came across this on Google from someone who seems to have had a similar problem:
1. Search for hpzsetup.exe file in all files and folders
2. Delete all instances of it.
3. Search for hpzsetup.exe in the registry
4. Delete only values containing hpzsetup.exe
5. Empty Recycle Bin
6. Restart Computer
(Don't edit the registry unless you are sure you know what you are doing though).
Final solution - try using System Restore to go back to a restore point before all this happened.
Alternative solution - just put up with it