I tried all of the tips listed in this thread without success. I have a Mac Mini 2.1 that meets all of the specs for App Store, etc. It even validated previously. However, I get the error listed in the title of this thread. In summary, I repeatedly deleted all the files, deauthorized computer, deleted ports, reinstalled OS, etc. However, it appears the crux if the problem is that my ethernet port on the mini is shot. As a result, it fails some type of hardware validation with the App Store. Luckily, on my iMac, I can login to App Store. Something I found was how to download and burn a copy of Lion to a DVD. There are multiple sites that explain this, but this one was most clear:
http://www.hightechdad.com/2011/07/21/how-to-re-download-mac-os-x-lion-create-a- bootable-install-dvd/