I had the same problem. Check the version of iTunes via the About dialog. Mine said 9.0.2 despite having upgraded via system updates, itunes and even downloading the whole package again.
Turns out, the dock iTunes link is running the old one. Basically, remove it from the dock, and re-drag the itunes from the applications folder back onto the dock. This then started 9.0.3 for me, and my iTunes account worked, the itunes store worked and iphone sync worked as well. Phew.
Check the bottom of this page for my reference
http://support.apple.com/kb/HT2311