I once saw a video of a Youtuber named Larry Bundy I think. He also had a lot of his collection in a shed and almost his entire collection was ruined by water damage because the shed had sprung a leak in it's roof.
Storing them in an outdoor shed is not a good idea. Out there ,your collection is exposed to heat and cold and moist air depending on where in the world you live in.
I wouldn't be surprised if some of your CD's or DVD' or even Blurays are no longer in working condition. Sorry this happen to you.
I guess you probably don't have anywhere else to store these games
but It would be better for you to store your collectibles in a heated or at least environment or somewhere in your home but never a garden shed again.