I've recently ran into the same problem with friend who had an HP printer as well. I think the activeX controls may differ based on the printer vendor but it does seem to be an issue with HP printers.
The solution is simple though!
Your most likely using the Internet Explorer icon labeled 'Internet Explorer (64-bit)' or a copy of that shortcut someone created for you.
To fix this, remove the shortcut from the desktop, go into the start menu -> all programs, and drag a copy of the 'Internet Explorer' shortcut to the desktop. (Not the 'Internet Explorer (64-bit)'!)
You should now be able to print!
Additionally, if you see a blank screen in the print preview feature then you might have a corrupt or missing 'Low' folder.
To fix this, click start, type %Temp% in the run box(With the percent signs) and then hit enter. Windows explorer should open up to your local temp folder. Tap your 'Alt' key so your Text menus show up at the top of that window and click 'File', then go down to 'New' then 'Folder'. Give it the name 'Low'. *Your account will need administrator privileges to do this.*