iTunes 12 will not play albums - just one song at a time
iTunes doesn't move to the next song by default, it moves to the next checked song.

If all are unchecked, that's your issue.

To recheck, in 'Songs' mode, select the top one, scroll to the bottom, shift/click the last one.
Right click > check selection.
[it might say 'tick' not check, I'm not sure if that's input language-dependant…
US check == UK tick]