Here is more information about the Event code 3004:
http://www.eventid.net/display.asp?eventid=3004&source=.
Although Windows Defender (WD) and Avast do co-exist, Avast is a strong AV that picks up more detections. I would recommend that you change WD to on-demand (when you need it), reboot, and test it out and see if this error goes away. Should you need WD in the future, you only need to update the definitions and turn the resident part back on. But there really is no need to have 2 resident AV's running.
Are you running the current version of Avast, which is 6.0.1125?
If you would like an extra back up, I would suggest an on-demand scanner like Malwarebytes (MBAM)
http://www.malwarebytes.org/ either free (on-demand) or Pro (one-time paid resident) that most of us use here and does not conflict with Avast.
Let me know if you have any other questions. Thank you.