Ok, sorry...it's been a long day; first, go to>Systems Preferences/System/Accounts and see if there is one & only one user with Admin priviledges enabled. This is kind of a longshot, but it happened in my case & iTunes was a mess until I figured out that there can only be one user w/admin privs.
Also, when you say you uninstalled it, what specifically did you do? Did you use a certain third party utility to facilitate the process or did you just delete/trash the ITunes app & files as best you could somehow?
The reason I ask is that to my knowledge uninstalling what is an essentially an integral, proprietary application such as iTunes (as opposed to say a third party app) is much easier said than done.
Tell me, about what % of your iTunes media files - be they music, video, podcasts, etc... are associated with "the cloud" (and could feasably be redownloaded)?
Finally, about what % of your iTunes media files do you have on a backup drive, or Time machine, or on discs burnt as backups?