Is anyone else having major problems with Intego Virus Barrier after installing El Capitan?

You should immediately uninstall all anti-malware software. You do not need it provided you are keeping up with Security Updates for OS X. In particular El Capitan has its own anti-malware software built-in. So get rid of the Intego software.

Uninstall your anti virus app.

Effective defenses against malware and other threats

Uninstall Intego

https://www.intego.com/manuals/intego-gettingstarted-mac-internet-security

There are no viruses that can attack Mac.OS X. So, anti-virus programs are selling a cure for a disease that doesn't exist. And they are renowned for borking Mac systems.

A Mac can pick up malware but not if you just use common sense. You really have to actively invite some malware in for it to happen. That means downloading and knowingly giving your password for it to download. Mac provides all the protection you need with SIP (System Integrity Protection).I About System Integrity Protection on your Mac - Apple Support

If you do happen to download adware you can use MalwareBytes to get rid of it. Malwarebytes was developed by one of our own colleagues here in ASC. It gets rave reviews and is about the most proven anti-malware software for Mac. If you use torrents, don't. Torrents are a good way to pick up malware because anything can hitchhike in on a download.

Safari pop-ups are different and easier to deal with. In Safari 9.1 and later just close the window. For earlier versions force quit and hold the shift key while restarting Safari.

https://support.apple.com/en-us/HT203987

Finally, stay away from programs that purport to "clean your Mac". They can do damage to your system. Your Mac needs no cleaning in the first place. All the cleaning that is necessary is taken care routinely by OS X.