Before this goes down this path too much further - I should probably clear up some misconceptions.
1. If your browser was in "Offline mode" - you would not be reading these posts or replying to these forums. Offline means not connected to the internet - view only pages etc that are stored on your local hard disk. It is extremely unlikely you would be able to set "Work Offline" by accident.
2. Antivirus software isn't likely to cause a problem as much as antispyware type utilities that might try to block a program writing to the registry. On a separate note - don't run more than one antivirus product in "real time" mode - as typically every single read and/or write to a file will be checked - and double or triple checking is going to slow your pc down and possibly cause conflicts as one antivirus might block access to a second antivirus program. (They make pretty poor room mates - both expecting to have the "top bunk"). Having additional Antivirus programs to run "on demand" or "manual scans" is fine.
3. Connecting via a proxy. Some ISPs suggest their customers use the ISPs proxy so they can cache web pages and data to improve performance for users requesting popular web pages (retrieve the page from the ISP instead of from the other site of the planet). Try changing your connection options for "direct connection to the internet" instead of specifying manual proxy settings (make a note of the proxy settings first - so you can set them back).
4. Port 80 is HTTP (The protocol used for web pages). No ISP is going to block port 80 outbound - unless they want to prevent their customers looking at web pages. If port 80 was blocked you wouldn't be reading this (or anything else for that matter). Not being able to activate a giveaway would be the least of your worries.
5. Not having Administrator rights. (For activation) so far I can't remember any giveaway this was required. Having admin rights to run the setup might be likely if the program modified some system-wide protected settings or wanted to perhaps update files in the windows\system32 folder. But normally all that happens with activate.exe - the program contacts the GOTD server to determine if the giveaway can still be installed (ie. has the giveaway expired?) and then writes some data into the registry (a similar sort of process that would likely occur if you manually entered a serial number into a program).
The point to remember is these settings for activating most programs are "per user". (Imagine that each user has a box of settings). For example - if I had a computer with 2 user accounts - admin, and fred. If you run Activate while admin is logged in - then the software will be licensed for the admin user - fred will see the software as a demo (if they can run it at all). This is why people have confused having admin "rights" and just being "admin" - If instead - I activated the software whilst logged in as "fred" then admin would see the software as being activated (despite having admin rights - he doesn't have the activated settings in his "box of settings".
It is handy to know - if you have a few accounts - and maybe an account for the kids - activate the game giveaway while logged in using the kids account - and a program in another account - the kids account won't see the program as activated, but the game will be.
Finally, I went back through some older messages I have from the GOTD team and found this explanation of the "wrong key" - unfortunately it doesn't go much further than we are at the moment.
The activation module can process almost every error during activation and display corresponding readable error message. The unique error which cannot be processed occurs if the data, which the activator receives from the server, has been modified during transfer (some proxy servers can do this); in this case user receives the message "The key is invalid".
So in english, activate asks the GOTD server "is this giveaway still active?". The GOTD server responds back to activate.exe, but the answer doesn't make any sense to activate.exe, and activate says "The key is invalid".
I'm not sure if a different error would occur when the server doesn't understand the initial query from activate.exe.
