I've added Summer Wars to my recommended anime list.
It is available on DVD and also on Blu-Ray
Here is the description I gave it in the list.
Kenji almost made it into a major math competition and instead expects to spend his summer break just doing his part time job as a low level administrator for the massive international network OZ. Then Natsuki talks him into working for her during the break at her grandmother's house for a few days. But things get complicated and Kenji is not only caught up in a small scheme of Natsuki's but ends up being suspected of being the hacker who cracked the security of OZ. Now things are really getting messed up and lots of people may end up dying.