Hi,
Sorry I didn't have more time earlier to elaborate. Let me see if I can help a bit now.
I don't think installing Flash would have necessarily caused your problem as this is presumably (since it's free) genuine software. My friend had previously run a copy of CS4 or CS5 and it wasn't genuine so it needed some modifications to the hosts file to prevent the software from validating itself. This is a pretty standard way to prevent software validation and activation but shouldn't be necessary for genuine software such as Flash. I should mention that my friend has long since got rid of his CS4/CS5 installation as it was overkill for his needs anyway.
Anyway, first things first. KeyChain first aid.
0. Let me cover my a$$ by suggesting a backup before you make any system changes. Time Machine or a Clone is fine.
1. Open "KeyChain Access" (either type "KeyChain" into Spotlight and select the app or choose it from Applications - Utilities - Keychain Access
2. From the system menu "KeyChain Access" (beside the Apple Logo top left) select KeyChain First Aid.
3. In the window that pops up, your username should already be entered so just type your password (login password) and select verify and click start.
4. If any errors are reported then click Repair and then start again to repair them. Hopefully this will resolve any issues.
Try FaceTime again.
If that doesn't work then try the steps I mentioned in step 2 on my last post. Here is the link again.
https://discussions.apple.com/message/15722416#15722416
If you need help with this then let me know and I'll try to give more details.
Try FaceTime again.
If that doesn't work then firstly, take a look at your hosts file and see if it matches mine from my last post. If you find it has loads of extra lines in it then come back to me and I'll try to help you fix it but you need to understand what the extra lines are for and I can't do that without seeing them.
To read your /etc/hosts file, do the following:
Click on Finder
Press Shift - Cmd - G to open the folder chooser dialogue.
Type /etc in the dialogue and click Go
Now look for a file called hosts and right-click on it (or Ctrl Click if you use a single button setup)
Choose "Open With" and then choose TextEdit as your application to open it. This may be the default anyway.
If the files is not the same as the lines I showed in my last post then copy and paste the entire file (assuming it is not huge) into a reply and I'll take a look. Editing the file is not quite so easy as it is a protected file which requires admin permissions to edit but we can cross that bridge if we need to.
Let me know how you get on with the above and if anything seems unclear. I'll be back online in 9 hours or so (9am BST). Good luck!
Craig.