find / -type f -print0 | xargs -0 grep -i pattern
This command will look for every file in the system and search a (case insensitive) pattern using grep. The file names are passed as arguments through xargs. You have to change the starting point of the search, depending on the mount point of the disk: in my example I put "/" which causes find to search in every little corner of your system.
Just two notes: 1) the command can take a long time, depending on the size of the filesystem, 2) most likely you have to run this command as root, to avoid some permission denied error. See man find, man xargs, man grep for future reference.