"It does not exist any more."

Translation: Den findes ikke mere.

[GC1998]

What is the difference between "den" and "det" when starting this sentence? I presume "den" is for "-en" and "det" "-et" words, so which one should be used when it has not bee defined yet?

[RyagonIV]

You're correct with your presumption. And you should know what you're talking about when you say that it doesn't exist. :D
But if you really have no clue whatsoever, use det.

[MarinaSo09]

why is existere not correct here

[petrenko]

I just typed 'det eksisterer ikke mere' and it was accepted

[Pippapips]

Any more (two words) is reserved for the meaning even the smallest amount. In other words, when used as a determiner, the two-word spelling any more is used.
Anymore (one word) is reserved for the meaning any longer. In other words, when used as an adverb, the one-word spelling anymore is used.
Anymore should be used here, I believe .

[RyagonIV]

Both spelling versions mean the same in regards to "any longer".