No problem. I liked the video link; did not know you could get a shuffle for the all songs list by dragging down, so thanks for that!
If you have shuffle turned off, it should play all songs in the playlist/album in sequence from your fist selected song onward. Unless there is only one song in the album/playlist: Then, if replay were turned on it would play that song again and. . .
All in all, I'm making assumptions about what is going on and could easily be wrong. I just picked the one thing that could both cause the problem and be easily overlooked.
My second suggestion if that isn't the cause is to perform a restart and then a reset (like you did) if that did not work. I suggest the restart first because Apple does, not because there have been any reports of problems from doing the reset instead. Instructions to follow, just in case the OP needs them.
Restart: Hold down the power button until the power off slider appears. Slide it off. When the iPad finishes shutting down, hold down the power button again until the Apple logo appears.
Reset: Hold down the power and home buttons until the Apple logo appears. The iPad will reboot. This usually takes a bit longer than a restart.