Personally, I think a petition to get a refund is a silly action. They're not going to refund people because I'm sure their legal departments made very sure that they never broke any law...
HOWEVER, I would've supported a petition to get a major gaming site like Kotaku to report on the remarkably poor customer service which gamers have received with this release. At the moment, the fact that some users couldn't play a game they paid for until 12 days after release... the fact that the entire upgrading system broke down for some people to the point of being unusable... the fact that the multiplayer was totally unplayable... the fact that PC users have been asking questions for months before the release of Crysis 2 and being outright ignored (particularly on issues that would've harmed sales... I wouldn't mind if they just came out and said "WE're not releasing Sandbox with Crysis 2 because we're concentrating on getting a good game out first. Sandbox will come when our development cycle has calmed down a bit", but instead PC users have been blanketly ignored)... and all similar issues... (EDIT: I forgot to mention the multiplayer that had like... no anti-cheat at all for two weeks

)
The only people who know about these things are people who are on the gamesas forums and have already bought the game. I would be very happy if a large gaming site brought attention to this to show that this is an inappropriate way to treat customers. EA locked out one gamer for 24 hours from his copy of Dragon Age 2 and it was on all the news sites... some people here were unable to play their game for almost two weeks.
Before people say "this happens with every major release", I'd say... then help stop it from happening in the future! Whilst this treatment of customers stays in the shadow, it will just keep happening every time. Perhaps if RockPaperShotgun, Kotaku or similar reported on it, it might give developers cause to pause... at worst, I'd expect one of these companies to come right out and ask Crytek for a direct answer on such issues as "Is DirectX11 coming?", "Are modding tools coming?" and similar. It's a lot harder to ignore when your "no comment" is going to be published on an international gaming site.
So... I'm not signing this petition, but if you start another one, trying to get 3000 signatures from PC users disappointed with the Crysis 2 after-purchase service to send to a few major gaming sites, PM me.