I can't enter on Skyrim giveaway due the free weekend, how to solve this problem?

Correct.

From what I know, there is not. This seems to happen every time there's a free weekend so I am going off of what I remember from those threads. If your account syncs when the free weekend game is on it, SG thinks you've got the game. I remember some people who played the free games having the problem for up to two weeks after, since the game would still be in their recently played list.