Chosen Solution

Just like the title says, reads dvds and blu rays just fine but I put in a game disc and nada, there is a slight click like right after it seems to read it but still nothing.

This seems like a problem with the disc reader because the Blueray and game discs use different readers. You might want to look into it a little more because I am not sure, but try this PlayStation 3 Slim Blu-ray Disc Drive Replacement

You need to make sure if the console hasn’t been repaired by someone else before. It is highly unlikely that it can read blu-ray but not games, this usually suggests swapped drive.