When trying to update applications, where can you find an account you used to purchase the application?

The App Store has had the little red notification saying I have two new updates to download, for iPhoto and iMovie, but when I go to download them it says "please log into the account you used to purchase the application." I am not sure which account this would be, as I have only had one account on my computer since I purchased it from the Apple Store online. 
Please help.
Also, a side note not related to this issue: I have been having problems with system preferences as well, when trying to change the background image the rainbow starts spinning automatically and then it becomes unresponsive.

Welcome to the Apple Support Communities
First of all, I suppose that you bought a brand-new Mac, right? If not, you won't be able to update iPhoto and iMovie, because they are registered to another Apple ID.
If you have a brand-new Mac, first try this > http://support.apple.com/kb/TS4236 If it doesn't work, check that iPhoto and iMovie aren't hidden on your account, so unhide them > http://support.apple.com/kb/HT4928 After doing this, try updating iPhoto and iMovie again.
If nothing works, contact with the App Store support > http://www.apple.com/support/mac/app-store/contact
Respecting to your second problem, your Desktop settings file is corrupted. To fix it, follow these steps:
1. While you are on Desktop without any application opened, select Go menu (on the menu bar) > Go to Folder, and type ~/Library/Preferences.
2. Delete "com.apple.desktop.plist" and "com.apple.systempreferences.plist", and restart

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