It's hard to know if you are reading things correctly. If, it's really 1.000 it is fermented and done. It likely started near 1.100. Grape juice that has not fermented, is incredibly sweet-meaning not subtle, you would know. So if you're thinking maybe you can or can't detect sweetness, it fermented. I have recommended before that people use a precision hydrometer for the end of fermentation. I use a +5/-5 brix hydrometer and you should too. The inexpensive triple scale hydrometers are not very accurate or reliable.
You may have a stuck fermentation, which is a different problem.
Don't give up on this yet, because you may be just fine. You don't really taste alcohol in new wine.