It's possible that the grape juice you used had sulfites in it, which does inhibit fermentation. It is also possible that it is fermenting just fine- wine typically does not explode like beer does when fermenting. Wine does not usually develop a krausen or a cap either. It's usually slow and steady.
A couple of things to remember- you must protect your must from air by using an airlock after primary fermentation. That is to say- I start my wines in a bucket, loosely covered with a towel to keep things from falling in. But I ALWAYS have used campden tablets first to kill bacteria and other undesirables. Then, when fermentation slows down (after a week or so), it goes into a airtight container with an airlock. An airlock works, but if you have a latex balloon, you can use that instead. Or post again or PM me, and I'll try to help with other ideas (a blow off tube, a flutter valve, etc) Because it's a slower ferment getting started, there is more of a chance for infection if you let air get to it- especially if you don't use sulfites or boil it first. Wine yeast is preferred over brewers or bakers yeast because it would be more tolerate of higher alcohol levels.
A good, simple recipe looks like this:
2 cans (11.5 oz) Welch's 100% frozen grape concentrate
1-1/4 lbs granulated sugar
2 tsp acid blend
1 tsp pectic enzyme
1 tsp yeast nutrient
water to make 1 gallon
wine yeast
Bring 1 quart water to boil and dissolve the sugar in the water. Remove from heat and add frozen concentrate. Add additional water to make one gallon and pour into secondary. Add remaining ingredients except yeast. Cover with napkin fastened with rubber band and set aside 12 hours. Add activated wine yeast and recover with napkin. When active fermentation slows down (about 5 days), fit airlock. When clear, rack, top up and refit airlock. After additional 30 days, stabilize, sweeten if desired and rack into bottles.
You're a little heavier on grape juice and light on the sugar, but it might equal out just fine. Acid blend is for flavor (to balance the acids) and pectic enzyme helps clear out haziness caused by fruit. Neither is necessary, but if you try a recipe like this next time, I think you'll be pleasantly surprised at the results.
If you are seeing activity (even slight), leave it alone and keep it around 70-75 degrees. You'll have wine when you're done, but the taste might not be great.
Instead of using your Mr. Beer to make wine, it's better to just use a one gallon glass jug with an airlock. You want oxygen initially to get to your must, and you don't have that with your Mr. Beer. The other thing, with your Mr. Beer, you WANT co2 to stay in the machine, because that's what carbonates your beer. You don't want carbonation with wine.
Happy fermenting,
Lorena
(I hope a moderator can move this to the right forum)