nor is there/there is

This is an idiomatic rule with "nor" when it's used to connect two independent clauses. We could say:

There is no food. Also, there is no water.

Alternatively, we could connect these with "nor":

There is no food; nor is there water.

For whatever reason, the subject and verb are inverted in this construction (much like they would be in a question). It would not be correct to use normal subject-verb order here.

Jim is incorrect about the use of "neither," though. In such a construction, when "nor" follows a semicolon, there is no "neither" in the preceding clause. We could (arcanely) say:

Neither is there food nor is there water.

In that case, though, we would not use a semicolon.