El-Hazard: The Wanderers (1995)

At Shinonome High School, Makoto, a mild mannered engineering prodigy is working on a special science project with some help from his girl friend, Nanami, an entrepreneurial whiz as passionate about her work as Makoto is at his. Unfortunately, her brother, Jinnai, a mega-maniacal cheat who irrationally thinks that Makoto is out to ruin his every ambition including his corrupt school presidency, has other plans. He tries to sabotage Makoto's device when Makoto catches him. In the ensuing struggle, the rewired machine opens a dimensional portal that throws Makoto, Jinnai, Nanami and their history teacher friend, Mr. Fujisawa into the world of El Hazard. Once there, Makoto and friends struggle to find a way home with all the help that a princess they meet, Rune Venus of Roshtaria, can give them as well the special powers granted to each of them as a by-product of the trip. At the same time, they must also stop Jinnai, who has allied with an enemy nation, called the Bugrom to conquer El Hazard.