aiizaztarliq21: I solved my problem, and here is how I did it. I don't know if it will work for you or not, but it's worth a shot.
1. Make the time zone on the Mac not automatic (but correct to your time and zone), and change something in that pref. pane so that it overwrites the old prefs file.
2. Log out of iMessages, iCloud, etc., on your iOS devices
3. Un-associate your Apple ID with your computer user login (in System Preferences > Users and Groups).
4. Sign out of iCloud on your Mac.
5. Reboot.
6. Re-associate your Apple ID with your user login. If you see a caution icon next to it, double-click. Should disappear.
7. Launch iMessages and attempt to log in.
8. Then log in to iCloud via System Preferences > iCloud
If that doesn't work, do these steps, then go back to # 1, above.
9. Delete all the Apple tokens and keys in the Keychain (might break some other things--may be why I can't log in via Safari right now).
10. Reinstall Mavericks/OS X.
11. Repeat steps 1–8.