I was having a similar problem that Applecare just helped me solve. I'll quickly describe what was happening and the steps to solving it.
Problem: I was unable to connect to certain websites on my iMac (using wired ethernet connection to Airport Extreme) in any web browser. Certain websites (Woot.com, Store.apple.com as examples) would behave as if I had no internet connection whereas others loaded fine. I could access these sites through other computers on my local network connected wirelessly without issues. I could also access them on my iMac through a proxy page. This started out of the blue, and I suspected my Airport Extreme. Turns out the computer was the problem.
Solution: I called Applecare (still had coverage for my iMac) and they walked me through the following steps, which solved the problem:
1. Open Finder.
2. Go to Home folder, Library subfolder, move Caches folder to trash.
3. Go to Macintosh HD, Library folder, move Caches folder to trash.
4. Go to Home folder, Library subfolder, preferences subfolder, move file "com.apple.Safari.plist" to desktop.
5. Quit all open browsers.
6. Restart computer.
7. Empty trash (this took awhile).
8. Open Safari.
9. From Safari menu (next to Apple icon in system bar), click Reset Safari.
10. Uncheck in dialog: Removed saved names and passwords, Remove Autofill form text, Reset all location warnings.
11. Click "Reset" in dialog.
12. Try to access the problem sites again.
For me, this solved the problem, both in Safari and Chrome. I'm putting it here in case it helps anyone else. I was not getting the same type of "Access Denied" error, but otherwise the symptoms were similar. Good luck, everyone.