Well, there are some original composers and artists exclusively on Youtube, to name a few there is DeStorm, Noisestorm and DjEphixa. As to songs that are only available on youtube, there is a large variety, but not many I can name.
I listen(ed) to Sonica - Dropship,Surface 2 air - Broken, Surface 2 Air - Inside Out,
Aim for the sunrise - Defender defeater, Adept - Sound the alarm, Sienna Skies - Sea of smiles,
Fox and the wolf - Bring me the horizon,Daidalosone - Square Garden, Aylius - Lucid,
Nightcore - Time of dance, etc. That were/are only available at youtube, because that's the only place where the published their music. In my opinion some really deserve more recognition, some are definitely hidden gems waiting to get discovered. Even though I only scratched the surface of what I listen to and the number of unheard songs and songs available only on youtube, I think my list will suffice.
Also a tip for helping people find their song; if you know the lyrics to a song, even if it's a couple of words, type it in google and 9 times out of 10 you will find your song. It helps if you know the lyrics to a chorus, as it's sometimes the title of the song, or it's unique.