VIDEO GIRL AI (Den'ei Shojo) by Masakazu Katsura. First published in 1989 and first published in North America in 2000.
PLOT:
Yota Moteuchi is such a hopeless dork with girls that when he tries to ask his crush Moemi out, he ends up helping her ask his best friend out instead. Heartbroken and ashamed at his own cowardice, he wanders the streets until he comes across a strange video rental shop. He picks up a promising title: "I'll Cheer You Up: Ai Amano." Yota takes it home and manages to jerry-rig his broken VCR long enough to play it, but somewhere some wires got crossed and Ai emerges from the TV into his room. In the video she was gentle and sweet, but now she's blunt and tomboyish with smaller endowments to boot. Yota can't complain when it means that someone can cook for him (even if she sucks at it), keep him company, and help him figure out how to win Moemi's heart, but what will happen when Ai starts to develop her own feelings for him?
