My Son purchased and downloaded a game on PS4. It says it is installed, but when He tries to play the game, it says insert disc???? HELP!!!!!

It would help to know what exactly was purchased. For example, the games that are 10 bucks via a code through the PS3 to PS4 upgrade thing will still require the PS3 disc inserted.

Now if what you are talking about is just digital game bought normally through the PS4, then the first thing I would think to try would be to delete the game and try downloading it again. Aside from that I wouldn't know what to try other than contacting customer support.