Appstore Windows 8 problem - error 0x80070032

Hi Peter,

Could you let us know about the complete error message?

Let us follow these methods and check.

Method 1:

 Run Apps Troubleshooter

 I would suggest you to download and run the Modern UI App troubleshooter.

http://download.microsoft.com/download/F/2/4/F24D0C03-4181-4E5B-A23B-5C3A6B5974E3/apps.diagcab

Method 2:

I would suggest you to place the computer in clean boot state  and check if you are able to download.

Clean boot: To help troubleshoot error messages and other issues, you can start Windows by using a minimal set of drivers and startup programs. This kind of startup is known as a "clean boot." A clean boot helps eliminate software conflicts.

 http://support.microsoft.com/kb/929135

Note: Please go through the section: How to reset the computer to start as usual after troubleshooting with clean boot of the Kb article to boot the computer in normal startup after fixing the issue

Method 3:

If you are unable to download apps in clean boot state, then I would suggest you to follow the steps given in the article.

What to do if you have problems with an app

http://windows.microsoft.com/en-GB/windows-8/what-troubleshoot-problems-app

Reference:

Why can't I find or install an app from the Windows Store?

http://windows.microsoft.com/en-US/windows-8/why-find-install-app-windows-store

Do let us know about the results, so that we can assist you further.