A kid who can't sing worth anything decides he's going to be a rock star anyway. The OVA doesn't pretend this is inspirational, it's messy, it's awkward, it's him failing in real time while the people around him actually have talent. By the end you're not rooting for him to win; you're rooting for him to keep trying, which is harder and more human than any underdog story that promises success.
Kazu 1-ban! is a 1998 music OVA.