Short answer: Your first sentence isn't correct at all. You can use either of the conjunctive adverbs to connect the two clauses, but they shouldn't be there together. Also, some believe it's better to use a semicolon to connect two complete sentences.
Long answer: Nevertheless and although are refereed to as [conjunctive adverbs]:
A conjunctive adverb is an adverb that connects two independent clauses. Conjunctive adverbs show cause and effect, sequence, contrast, comparison, or other relationships. (Emphasis mine)
Either of these options is fully correct:
Although I would like to start, it is not possible.
Or
I would like to start, nevertheless, it is not possible.
But wait...
This is rather pedantic, but some people (including the author of this tutorial) believe that if you are to connect two whole sentences, a semicolon is preferred over a comma.
So, the fully correct sentence with nevertheless is:
I would like to start ; nevertheless, it is not possible.