Photosmart C8180 stopped working and refuses any re-installation attempts on XP Desktop

Question

Hello, I am new to the forum and am in need of some installation help.
I had graphics card failure (twice), and the last time the computer got turned on it was without the printers USB being plugged into it and this seems to be when the printers Software Solution Center stopped working.  I could print in a mundane mannor but needed the solution center for my high end digital printing jobs.
So, I uninstalled and tried to re-install the software. Each attempt has given me a failed installation. I have been at this for days.  I got a fatal error but didn't see an actual code for it.  I allowed it to scan for problems and it told me "A solution has been found for this particular problem" but following each of those steps did not solve anything. The downloaded software from the site gave me the same results.
What happens is the software installation goes to approx 97% (although the last attempt said 100% and still failed) and then it hangs and says it took too long to respond. This part I failed to pay proper attention to, I believe. Sorry for the lack of better info here, but the software kept telling me "No HP devices have been detected" on each failed re-install attempt ... which have been at least 10!  I believe this is because the software didn't finish the install.
I ran disk cleanup between each retry as well - however I know for a fact all things were not removed from registry and found several folders in the Temp folder after as well. I didn't know what was safe to remove and what wasn't so left them alone.
I did get a screenshot of the Error Situation Code from the error log it prepared to send to HP and which is what prompted the  "A solution has been found for this particular problem" message and download of an app called HP Installation Error - XP.hta. Again, attempts to do these steps also failed.
I am at my wits end and hope to be able to solve this issue. I need my printer soon (I am making wedding invites "soon").
Here is my screenshot.
Thanks for taking the time to read this.

Answer 1

First:  I am a bit disappointed that it has taken over a month for a reply. I all but gave up.
I followed these instruction at the link provided. However, I couldn't follow through -
When I clicked on the HP Update link provided, I choose XP, selected Next, clicked the plus sign next to Update (It only showed Update(6)) I do NOT get an option anywhere for "HP Update Software Utility".
All I get are these:
1. Critical Update: Cannot find scanned image or document files after scanning completes.
2. Solution Center Update
3. HP Print Driver Update
4. Critical Update to Enhance Reliability of Network and USB Connectivity and Improve System Responsiveness While Printing
5. Critical Update to Correct a PC to Printer Communication Issue
6. Critical Update for HP Photosmart Essential
I do not understand what is even going on with this software! I have installed/uninstalled many times. The last time I got as shown in images in above messages. The software hung at the 96% mark on the final configuration. I went through all the steps shown in previous messages to troubleshoot. Followed all options given. Nothing worked.
This time I did not uninstall the software. It is listed in Program Files. It is listed in the Registry. The monitor icon is in the sys tray and is showing a green checkmark as seen here:
When I try to open Solution Center I get this message:
I can still use the printer (have not tried the scanner - its an Photosmart C8180 AIO) but cannot access advanced features.
I can access Photosmart Essentials. When it first opened it asked to check for updates. I thought I would just to see if the software was working. This is the message I got:
BUT, as you can see - I am online already! What is up with that?
While going through some of those steps provided in the link you gave me in the above message I went into Event Viewer to see what I could find. I cannot believe after all the years I have used the computer - I never knew about that!
Interesting information. I found many error messages and warnings (for a total of 21!) in there related to the HP install attempts. Many are repeats because of the sheer number of times I uninstalled/reinstalled. All contained either an error code of 1904 or 1905. Each showed an issue with either Flash (filed to register), smartwebprinting (ClipBook.dll not existing), etc. I am going to give screenshots of the ones that seem to be different (bare with me here):
OKAY ... That was all the messages. You can see on them which were fatal and which were warnings.
NOTE: About the one showing an error with the Flash. Flash is installed and it is the latest version. I do not recall if it was at that time (since this has been over 30 days ago), and as I said - I have not tried to reinstall again .... I cannot begin to tell you how discuted I am with HP 'anything' at the moment.
I hope I have not left anything out after all this time. I have tried to provide as much information as possible. I hope to hear back; soon.
Thank you.