Translation:He cannot sleep because of the beautiful woman.
"Vanwege" is like "because of", not because. Want is like "for" in English, it's a coordinating conjunction. In Dutch, the word order with "want" doesn't change like with "omdat" and "doordat". So basically "want", "doordat", and "omdat" are interchangeable, but "vanwege" isn't because it's "because of". Sorry if this is confusing.
Note that "vanwege" is a preposition, whereas "want" and "omdat", etc., are conjunctions.
The clause following a conjunction will contain its own verbs. (And in Dutch, the conjugated verb will come at the end if the conjunction is a subordinating conjunction like "omdat").
But the phrase following a preposition does not contain a verb -- just nouns, adjectives, and/or adverbs.
• Vanwege= because of, due to
• want= because. It's a coordinating conjunction, so there's no change in the word order:
Ik moet naar mijn bed kruipen want ik ben moe.
• omdat= because. As it's a subordinating conjunction, the verb of the subordinate clause must be placed at its end (I mean, at the end of the sub. Cl.)
Ik moet naar mijn bed kruipen omdat ik moe ben.
Omdat ik moe ben, moet ik naar mijn bed kruipen.
Note that in the second example there's subject-verb inversion in the main clause (Ik moet naar mijn bed kruipen). That's because we started the sentence with something other than the subject (we began with a subordinate clause in this case), and as Dutch is a V2 language, the verb of the main clause must always be the second constituent/element (note that I didn't say 'word'!).
• Aangezien= because. It's subordinating conjuction, so the same as with omdat applies:
- Ik moet naar mijn bed kruipen aangezien ik moe ben.
- Aangezien ik moe ben, moet ik naar mijn bed kruipen.
Hope this helps!
Oh, I forgot to add:
As they all mean 'because', omdat, aangezien and want can be used interchangeably, just be careful with specific word order that corresponds to each of them.
But, given the fact that vanwege means something else (because of/ due to), you cannot use it where you'd use want, omdat or aangezien (and viceversa).
In Dutch, infinitives (like "slapen"), as well as past participles and finite verbs, often come at the end of a sentence or clause.
However, Dutch often allows prepositional phrases (here the phrase is "vanwege de mooie vrouw") to be placed after the verb -- tacked onto the end, so to speak.
Dutch is more relaxed about this than German, but even German sometimes allows it.