Unable to use Apple ID on alternate user

Okay, the title of the question is a bit vague, but please bear with me.

Recently, I created a new user on my laptop (Macbook Pro, OS X Mavericks) and set it to administrator. So now I have two user accounts.

On my new account (let's call it Account #2 and the old one Account #1), I logged into Apple.com with the Apple ID I registered Account #1 with, but then I discovered I was unable to do anything. By anything, I mean everything. Posting and replying to posts I've made on Apple Support Communities fails to work, and I can't even log into the AppStore/iTunes with this Apple ID. I switched back to my other user account to see if it was a bug, but it worked perfectly fine (e.g. I could post, access the iTunes Store using my account... etc).

How do I solve this problem? It can be frustrating to have to use the Apple.com website using my other account, as I plan on using this user more often than the other.