I think you need to contact HP and ask for a way to reinstall your software
If at the end of
Local Disk C
Adobe Premiere Elements 10
you have 0 bytes
Then time for a complete uninstall/ccleaner run through/reinstall. But, what is the history on all this...have you been using the program successfully until this time and suddenly this major issue? When did you get the HP computer with pre-installed programs? Can you associate any catastrophic computer happening with this present situation?
If you do not have a backup nor serial number, System Restore sounds like something to try. Whether it will work is another story.
Did you register your Premiere Elements 10 with Adobe? If so, go to the Adobe web site http://www.adobe.com, sign in with your Adobe ID and password, and look to the top right of the home page to where it says My Adobe. Click on that and go to My Products and see if you can find your Premiere Elements 10 there with a serial number.
If you can produce a purchased serial number for your Premiere Elements 10, free tryout Premiere Elements 10 installation files can be obtained and your purchased serial number inserted in that tryout.
But the plan hinges on you having purchased serial number.
You would need to uninstall your problem Premiere Elements 10 and do the ccleaner run through before trying to install the Premiere Elements 10 tryout cited above.
Please review. Any questions or clarification needed, please ask.
Also determine if you can get Premere Elements 10 installation disc from HP.