Table sugar + fruitjuice + yeast not fermenting

I agree that keeping an opened packet of dry yeast at room temp for some time will decrease the viability of the stored yeast. Maybe a hydration mix or growing on in a starter might have helped but it would have been preferable to use new yeast.

Many yeasts will metabolise sucrose (table sugar). It is cleaved and converted to glucose by sucrase and invertase. But better than sucrose is glucose. It is preferentially catabolised by the yeast. Glucose/dextrose/brewing sugar can be bought in 25Kg sacks as well as smaller amounts from Brewing/HomeBrew suppliers. IIRC 8Kg is required for 24L of mash. They say fermentation can take 48 hours but be prepared to wait 5 days.

I presume the fruit juice was to add some form of nutrient as much as any extra sugars or flavours. Some fruit juices are pasteurised (which is OK for yeast) and some contain metabolite inhibitors ("preservatives") which will not be optimal for fermenting - but they often work if enough yeast is added.

That said, if one is simply brewing mash for distillation then a good idea is to use glucose and a pack "Alcotec turbo yeast" (or similar) - also available via Amazon. The turbo yeast contains all the nutrient needed to get 24L to 21% ABV as well as the high tolerance yeast. Some packs even contain activated carbon to add to the brew to boost it up to nearer 24% ABV. It is usually more efficient and cheaper than buying fruit juice and sugar.

I think you have already answered your first question yourself, if you think about it. You said your yeast went crazy, so it did not have any problems, nutrients were not needed.

However, keeping your dry yeast for four months outside a refrigerator is probably asking for problems. A whole lot of yeast has already died, and so you get a slow and stuck fermentation. If you had kept it refrigerated, then you would probably had a much better fermentation. I have used open yeast packet, refrigerated, from a year old. Also, always remove as much air as you can from the container where you store your yeast.

To get your fermentation going again, you should do the following things:

1. Rack your current beverage off from the old yeast into a new vessel
2. With new yeast and some apple juice, make a starter. Take your time, and give this a swirl every a couple of times in an hour
3. Add this starter to the rest of your beverage

The problem with the fermentation on top of the old yeast is that this yeast sends out chemical signals that inhibit further fermentation. That is the reason to first rack the current fermentation into another vessel.

Take care of sanitation of course.