The simplest way to deal with the problem is to edit the "start" registry, in particular the .exe line that refers to the HP software.
There are many tools available to download, to make editing simpler (if you are unsure of how to navigate the registry), here's one I use.
Regcleaner!
After unzipping and installing, open and run. Click on "start up list" at the top and look on the list to find the file in question. Select that file and that file only.
Remove it from the list. After that exit out of regcleaner and reboot to see if the problem has been corrected. Assuming it is, then head to "program files" located on your main drive partition. Find the folder for HP relating to the software you no longer have and "delete" it. Your done!