I tried to login to my account to snag this for free on April fool's day but I didn't know my password. I was away from home and couldn't get that information. Now, I'm back home and the giveaway is over? WHOOSH!!! Come on, man. Do this again!!! Or somebody can gift me a key, maybe? I don't how this GOG works!

The giveaway was running for 48 hours so there was enough time to get a free copy. You only have yourself to blame when you missed it.

Please don't be like that, have some decency.

I don't think it's cool to request a game, even if someone could have a spare key from the temporary giveaway. Considering you had to click over the URL inside a banner and you were never instructed to open the page below, I'd say it's impossible to send gift (containing XIII) to another user, or illegally sell XIII keys from the giveaway, in shady websites.
https://www.gog.com/redeem

https://www.gog.com/forum/general/the_community_giveaway_gog_edition_redux/page1 has multiple XIII keys that you can get, but you'll need to ask finkleroy if you can be eligible, since you are a new poster on the GOG forums.