LED's are polarised. They need to be connected the right way round to work. Plugging one into GND & pin 13 is not a good idea on an arduino made in the last 5 years (including the Uno). There is no current limiting resister in circuit. Its completely unnecessary any way, any arduino made in the last 5 years (The Uno) will have one on board, already wired and working. Its usually labelled 'L'. The tutorial you've found is out of date and doing it today can damage the Arduino. You may have already damaged the output on Pin 13.
Further delving, I realise now what I did wrong. Though I won't do it again, I was curious as to why even if you shouldn't do it (and believe me I won't do it again based on your advice) why it was working on a couple of the tutorials and not for me.
Thanks for your help (and more importantly, the warning!)