I have Premiere Elements 10 on Windows 8 64 bit, and it works very well. Also, have Premiere Elements 11 on that same computer. It also works very well.
We will need more details on specific situation, but let us first go through a check list. Please excuse if I ask questions where you have been there and done that. I just do not want to take anything for granted.
1. Do you have the latest version of QuickTime installed on the computer with Premiere Elements 10?
2. Are you running Premiere Elements 10 from a User Account with Admnistrative Priviledges?
3. Is your problem the type where "it never worked" or one where "it worked before but not now"?
4. What is happening in the project when the problem occurs, Including how much you have on the Timeline when the problem occurs?
5. Could you elaborate on what you mean by "AMD Screen" stopped?
And, depending on your answers to the above
1. What are you setting as the project preset for your project?
2. What are the properties of your source media?
3. What are your export goals for the Timeline content that you establish?
And, about your computer (even new and top of the HP Line),
1. How much installed and available RAM
2. How much free hard drive space? Is all your hard drive space from the Local Disk C or do you have supplemental drives (internal or external)?
3. Are your video and audio card drivers up to date? Good to check with HP just to make sure.
4. Is your computer optimized..ccleaner for regular and registry, defragmented...?
5. Do you have any other video editing or resource demanding programs on this computer?
Let us start here and then decide what troubleshooting strategy we need to develop to resolve your issues.