Ok I've found it on our Channel 4 which has a website 4OD that plays all the episodes it's already shown but I don't know if it will play for anyone not in the UK.
Apparently it's on series 6 here but if you scroll down a bit you can see the previous series so if it does play for you you can watch it from the beginning
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Apparently it's on series 6 here but if you scroll down a bit you can see the previous series so if it does play for you you can watch it from the beginning
http://www.channel4.com/programmes/st-elsewhere/4od
Like I said I have no idea if it will play outside of the UK but you can have a look see just in case.