Wow, that is pretty odd, but I am glad it works. You probably could have just started that program and changed the options to not run at Windows start. It might have even been listed in the Start Menu Startup folder from where that shortcut could have been deleted. Either way, clearly, if all works now, that program is not needed. Stuff like that is actually why I said in my last post to skip any extra software HP might want you to download with the driver. I suspect when you first installed this printer, you installed the necessary drivers from the installation disk that came with the printer. I never - as in NEVER EVER do that just because they (printer makers in particular - not just HP) always want to foist a bunch of extras we just don't need, like that HP Smart Install Utility. I note I have an HP PS 7525 and I don't even have an HP folder under Program Files or Program Files (x86) on my drive. I went out to HP when I bought the printer and downloaded and installed the drivers only file.
Any way - that was a learning experience - always a good thing. I am glad you got it sorted out and thanks so much for coming back and posting the solution! :) I will mark this thread Solved as requested.