Go to the iTunes folder (wherever you keep it) and Get Info on it from the File menu. Under the Ownership section, make sure you can Read & Write and that you're set as the Owner. Click Apply To Enclosed Items and see how it goes. I'm basing this off Tiger, but I don't think the Panther layout was all that different.
The weirdest thing happened, I updated, my iTunes, I forgot to, and now it opens. But now I need a way to get Calculator.app back, I think the "genius" at the Apple store deleted it. (but I figured out about 5 days after)