First off, there is the Minneapolis/Eau Claire/Raleigh-Durham supergroup GAYNGS performing "One More Try" with Har-Mar Superstar on vocals. While I'd have personally preferred to roll with Mikey Noyce on vocals, this is what I've got for you. Also, I really wanted to find a video of them covering of "By Your Side," "Cry," or "Eye in the Sky" with good sound quality but that wasn't in the cards.
What you get instead is a cover of the soulful George Michael mega-hit "One More Try" from his massive 1987 solo album Faith.
When searching for the perfect GAYNGS live cover, I also stumbled across this video of Iron & Wine covering "One More Try" for an Onion A.V. Club covers series, A.V. Club Undercover 2011. While taking a much different approach than GAYNGS, each group clearly shows a sincere affinity for the song.
If, for some whacked out reason, you don't know the original, here it is: