Fortunately you can fix this problem without reinstalling/retyping your serial number.  ”I found a solution after much searching online.

I downloaded QuickTime 7.6.6 from Apple.

I opened the DiskImage.

I downloaded the application Pacifist. And used this program to open the Package file inside. I found the plug-ins and extracted them to /Library/Internet Plug-Ins.

The problem was that QuickTime Plugin.plugin and QuickTime Plugin.webplugin were accidentally deleted. I tried to reinstall QuickTime from the Mac OS X DVDs and from standalone files from Apple, but for some reason the plug-ins weren’t installed into /Library/Internet Plug-Ins.”