Problems with reinstalling Photoshop elements 8 on a new computer

I didn't management to fix it. I hade to by a new version of PSE. 

i'm assuming your new computer is compatible with pse 8  (and therefore the answers to @AxelMatt 's questions won't reveal a problem),  because you've already installed it once on the same computer.  now, you need to properly uninstall (if that wasn't already done) and, from your description, you need to "clean" before reinstalling.

so, start here and follow the steps carefully, https://helpx.adobe.com/photoshop-elements/kb/elements-installation-error-CC-cleaner-tool.html

Mac or Windows?

IF Windows

Two ideas that MAY work to install and/or run old programs in Windows 10 or Windows 11
-RIGHT click the program icon or EXE and select a compatibility mode in the pop up option window
-and/or select Run as Administrator to assign FULL Windows permissions
-also https://helpx.adobe.com/x-productkb/global/create-local-administrator-account-windows.html

Please Consider including the following in your question:

• Operating system and version number
• The full text of any error message (s)
• Computer hardware, such as CPU; GPU; the amount of RAM; etc

Thanks. The above info will help to solve your problem.

PS Elements 8 is a 13year old program and not compatible with the new operating systems. It seems that could be the problem.