One little point about the fermenting process. The reason wine and beer primary fermenters have air locks is to exclude mold, fruit flies and oxygen. When O2 is present in the mash the yeast will produce more MeOH, aka methyl alcohol aka wood alcohol.
If you shake your jug around without opening it first there will be no O2 present and you're just stirring it up with the CO2 in the jug. Try adding a couple of tablespoons of sugar and see if it perks up. If it does that means the yeast hasn't made enough alcohol to poison itself yet and can go a while longer. If it doesn't perk up then the yeast is dead and you need to start over. To make it easier to drink without distilling, freeze the jug solid then invert it over a bowl and let it thaw for a while dripping into a bowl. Once you have a quart from a gallon jug you should have all the alcohol. Bread yeast will make up to 14%, wine yeast 16%, while champagne or distillers yeast can produce up to 22% alcohol before it dies off from alcohol poisoning. I have a 5 gal version perking in my grow room that is about done and I'm going to triple distill and carbon filter that sucker for 95% alcohol for tinctures and a few good piss-ups. I use 11.5 lbs. of sugar, 2 packs of wine yeast and a Tbsp. of yeast energizer and it perks away for 3-4 weeks. The next one I'll measure the amount of CO2 it produces and get a rough estimate of the CO2 ppm in my room with the exhaust fan off.
Oh yeah. Check the pH as it won't perk if it's too low. 5-6.5 seems to work good. Also check out homedistiller(dot)org for lots more info and recipes.