Your iPhone "thinks" you are doing something that is no ringer related. At present, based on your screen shot, I would guess it thinks you are playing music.
The reboot helping is a clue to that fact. Since a reboot stops all background audio tasks. Just for the grins and giggles, try the following.
Double click the home button.
Hold down the first app till it wiggles.
Touch the red - on every single app till they are all gone.
Hit the home button once.
Then adjust the volume up and down.
If the Ringer reappears it was an app stuck in background. You get to have fun finding which app it is.
If it doesn't, then you need to do a full back up and restore because you have something wrong with your software.