Problem signing in to Mac App Store

I am unable to login to the App Store with my Apple ID. I get "An unknown error has occurred". However, my Apple ID does work for the iTunes Store and for this forum.

I have two Apple IDs — one for UK and USA, and the other for Singapore. I've tried both. Both work for the iTunes Store (though they sign me in to different versions of the store), neither works for the Mac App Store.