Take your time. I will be available to help you after the weekend (Monday) but if you have any problems over the weekend, here is a link to help you with the instructions I have given you:
--HP Solution Center Failed to Install-- A lot of the questions you could have are likely answered in this 14 page thread.
Try this first!! --Solution Center Fails to Install-- This link includes an update to try first if you would like an easy task to try before you get started on anything too difficult. After reviewing your problem the last few days and thinking really hard about it. Try clicking this link to go directly to the HP Solution Center update before doing any uninstalls. I really think this will work!
I will keep looking for additional information to help you further. Keep me posted on how it goes!