Open Console in Utilities & see if there are any clues or repeating messages when trying to open iTunes.
Are these Flash Videoes?
Out-of-date versions of Adobe Flash Player do not include the latest security updates and will be disabled to help keep your Mac secure. If Safari 5.1.7 or Leopard Security Update 2012-003 detects an out-of-date version of Flash Player on your system, you will see a dialog informing you that Flash Player has been disabled. The dialog provides the option to go directly to Adobe's website, where you can download and install an updated version of Flash Player.
If you need to re-enable an out-of-date version of Flash Player, you can do the following:
1. Navigate to the /Library/Internet Plug-Ins (Disabled) folder.
2. Drag "Flash Player.plugin" into /Library/Internet Plug-Ins.
3. If the browser is running, quit and restart it.