There's always a reason for a non-starter - working out what that was is a problem

But are you completely sure it didn't ferment while you couldn't see it (that can happen if the airlock doesn't provide a complete seal)?
First things first, though - smell it. Does it still smell OK? No bad egg or rotting cabbage type odours? If not, it should be startable and non-toxic. Now, taste it - hopefully it will be sickly sweet and that will confirm your suspicions. If it tastes like wine, then it confirms that it DID ferment.
So, let's begin with the usual lecture - no-yeast recipes are chancy and, in my opinion, not worth the risk, especially if you live in an area where the wild yeast population is not famous for its efficacy. End of lecture.
Now to the problem, which may have been caused by old yeast, too-high temperatures, or sheer bloody-mindedness on the part of the wine fairies. Get yourself a clean bottle or jar and put a couple of teaspoons of sugar in it. Now take a couple of tablespoons of the non-starting wine and add it to the sugar. Add a small squeeze of orange or lemon juice (really - just a small squeeze) and then top up with a half-pint of tepid water (round about body heat is perfect). Add a level teaspoon of your yeast and then give the whole thing a damn good shake (you're trying to get oxygen into the liquid). Put a stopper or lid on the bottle or jar LOOSELY. Put it somewhere warmish and go and have a cup of tea.
A couple of hours later, take a look. You should see little bits of yeast rising and falling in the liquid. If you can't see this after 24 hours, your yeast is defunct and you need a fresh batch to begin the whole procedure over again. If you do see it, wait a few hours for a decent colony to build up and then dump the whole lot into the wine (you may have to take some of the wine out if you overfilled your demijohn).
The fact that you started the yeast with some of the original must in the liquid will give it a whole lot of tolerance, so your fermentation should now begin in earnest within 48 hours. If it fails again, then there's something seriously wrong with the must, which is unlikely.
Best of luck
Mike