After updating to El Capitan, I lost the ability to log into my Apple ID through iTunes. Nothing would happen when I tried to login from the store menu or the top of the main iTunes window. The App Store and everything else that requires Apple ID worked fine but no luck in iTunes proper. This made syncing apps, making and transferring purchases impossible. I did my homework on the issue; no serial number problems, killing processes didn't help. The solution that has been mentioned elsewhere, that also worked for me, was to reinstall El Capitan. Fortunately, this is a very simple process and took less than 30 minutes to complete.
Boot from the Recovery Partition (hold down command - R on startup)
Select Reinstall OS X from the list of options
That's all there was to it. Everything else on the disk remains untouched, Documents, Music, Etc.
When I started iTunes, I clicked on Sign In, and was able to do so with no issue.