An old anime with a scene of a young man struggling to reach the top of a glass staircase
A simple googling of the terms "anime glass staircase" brought me to a discussion page on:

Video Girl Ai (1992)

The scene is from Episode 6, the last episode of the OVA, and the only thing not matching your descriptions is that the staircase is not spiral: it is straight.



Synopsis (ANN):


  Because Youta worried for another instead of dwelling on his own broken heart, he happened upon a very special video store that only the pure of heart can see. There, he buys what he thinks is a normal erotic video - until a girl climbs out of his television set. Her name is Ai, and thanks to a broken VCR, her personality is a little glitchy. Still, it's her job to help Youta feel better, and perhaps even help him get the girl of his dreams, even if Ai herself might be falling for him as well.