Learn Hardcore German: Dank dem Regen ist der Park nass. - Thanks to the rain, the park is wet.

In modern German Dank functions as a preposition that takes the dative in everyday language. So you say Dank dem Regen. Historically it could govern genitive, but in spoken and informal writing you almost always use dative.

Is Dank des Regens also correct?

Yes. Dank with genitive (i.e. Dank des Regens) is perfectly correct and sounds more formal or literary. You’ll see it in newspapers or books, but in conversation people prefer Dank dem Regen.

Why is der Park in the nominative case?

Because der Park is the grammatical subject of the verb ist. In German the subject must be in the nominative case.

Why does the verb ist come immediately after Dank dem Regen?

German follows a verb-second (V2) word order. Whichever element you put first (here Dank dem Regen), the finite verb (ist) must occupy the second position.

Can I start the sentence with Der Park instead?

Absolutely. If you move Der Park to the front, the verb stays second:
Der Park ist dank dem Regen nass.
This simply shifts the emphasis onto der Park.

Can I drop the article and say Dank Regen ist der Park nass?

No. A singular noun like Regen generally needs an article after a preposition. You could use an adjective in genitive, e.g. Dank starken Regens ist der Park nass, but Dank Regen alone sounds ungrammatical.

What’s the difference between Dank and wegen?

Dank implies a positive or neutral cause (like “thanks to…”).
Wegen is neutral but often used for negative reasons (“because of…”).
Both prepositions take genitive in formal contexts and often dative colloquially (e.g. Wegen dem Regen).

Are there other ways to express the same idea?

Yes. You can use aufgrund, which always takes genitive:
Aufgrund des Regens ist der Park nass.
This phrasing is more formal than using dank or wegen.