I had the same problem with my mid-2010 Macbook pro. I could see and do everything on my local network, either wired or wireless but my Macbook could not see the Internet, including mail, Safari, App Store, etc. I never have had AVAST on any of my Macs, and my early-2008 macbook (still running SL 10.6.8) could connect wired or wireless to the internet, so I knew that something was amiss in the upgrade.
After reading through all the suggesstions did what someone else suggested: I went into System Preferences, turned off the firewall, rebooted, checked and was able to connect wired and wirelessly, went back, turned the firewall back on, rebooted, and I'm up and running. Local network and internet (wired & wireless) work seamlessly now.
I have rebooted several times and everything connects like it should.
I thank you all for your help and suggestions.