.hack//The Movie: Sekai no Mukou ni

Although all her high school friends are playing "The World", an online role playing game, Sora Yuki is reluctant due to her grandfather who seems to be avert to technology. Things change once she finds out that he secretly started playing this game. Now with no restrictions and with the help of her friends, she timidly enters the game and is thoroughly impressed by it. While still learning the basics of how to play, she witnesses an odd event: a mysterious girl being attacked by a smoke-like entity. The girl has no problem in avoiding its charges, but while doing it she approaches Sora and gives her a strange small cube that enters her online body. From then on, news start to appear that some players are losing consciousness while playing "The World".

Synopsis from Anime News Network