Very good, very wise.
Solution One: I want to try to repair the trayapp.msi which can be found by typing %temp% and searching for a 7z... folder containing your printer files (mine was called 7zS3AE6). Trayapp.msi is the file you will need to find in your setup folder. When I found it, I did one left click to highlight it and then right-click over it to repair it. Next try to open Solution Center.
Solution Two: If that doesn't work, check your Program Files for the hpscanapp.exe in the Bin folder (under HP>>Officejet 6500 E709 folder) to by-pass Solution Center and try to scan. I do not have this printer so I cannot finish installation but that is where this file is located I am certain. However, I am not certain that is how hpscanapp is spelled just know you are looking for an executable file maybe called hpschanapp.exe or something similar. If this works, save the scanapp.exe as a shortcut on your desktop.
Solution Three: If that doesn't work, rReview the document below for more some more tips.
Solution Four: Lastly, if none of the above suggestions work, go into safe mode and then open the 7z folder in your %temp% directory again and go to the Util>>ccc>>Uninstall_L4.bat which is a level 4 uninstall (not safe for HP computers). After the level 4 uninstall, search the entire computer for HP icons, folders, and any thing else left behind (this should remove keys in the registry for you, just check your Devices and Printers folder, for example). Then try to re-install again in safe mode with networking on so you can install your wireless printer. See Solution 3 in the link below for what to turn off (startup services, MS updates, etc).
--Fatal Error 1603-- I saw this error in your list above but I am still providing this only for more instructions on what to do next (starting at Solution 3).
This is the most comprehensive uninstall, re-install, and work-around steps I could think of to cover all possible troubleshooting in one post. Take your time. I have listed 4 different possibilities to try so I do not expect you to do this in one night. I have posted the easiest step first. Start there. My fingers are crossed the easy step works.