Billetautomaten ved indgangen virker ikke, så vi går til en anden automat.

Danish very often forms compound nouns as a single word, where English would use two words.

• billet = ticket
• automat = machine / vending machine
• billetautomat = ticket machine
• billetautomaten = the ticket machine

The -en at the end is the definite article, so instead of saying the ticket machine as two words, Danish says it as one word: billetautomaten.

Because Danish usually adds the definite article to the end of the noun.

For common-gender nouns:

• en automat = a machine
• automaten = the machine

So:

• en billetautomat = a ticket machine
• billetautomaten = the ticket machine

This is one of the biggest differences from English: Danish often puts the at the end instead of before the noun.

Here, ved means by, near, or at.

So:

• ved indgangen = by the entrance / at the entrance

It tells you the location of the ticket machine.

In other contexts, ved can have other meanings too, but in this sentence it is simply about physical position.

Indgangen means the entrance.

• en indgang = an entrance
• indgangen = the entrance

In this sentence, it is a specific entrance, probably the one everyone can identify from the situation. That is why Danish uses the definite form.

So:

• ved indgangen = at the entrance / by the entrance

Virker ikke means doesn’t work or is not working.

• virker comes from at virke = to work / function
• ikke = not

So:

• Billetautomaten virker ikke = The ticket machine doesn’t work

This is a very natural way in Danish to say that a machine is broken or not functioning.

In a normal main clause, Danish usually places ikke after the finite verb.

So the pattern is often:

• subject + verb + ikke

Example here:

• Billetautomaten virker ikke

Compare:

• Han kommer ikke = He is not coming
• Jeg forstår ikke = I do not understand

This is different from English, where not often goes with do/does/did. Danish does not need do in this kind of sentence.

Here, så means so.

It connects the two parts of the sentence:

• Billetautomaten ved indgangen virker ikke = The ticket machine by the entrance doesn’t work
• så vi går til en anden automat = so we go to another machine

It shows result or consequence: because the first machine does not work, we go to a different one.

At gå til here means go to.

• vi går = we go / we are walking
• vi går til en anden automat = we go to another machine

The preposition til is needed because there is a destination.

Compare:

• Vi går = We’re walking / We’re leaving
• Vi går til stationen = We’re going to the station

Because automat is a common-gender noun, so it takes en.

• en automat = a machine
• en anden automat = another machine

Anden means other or another.

So:

• en anden automat = another machine / a different machine

This is very natural Danish for choosing a different one from the first.

Because the form of anden/andet changes with grammatical gender.

• en-words (common gender) take anden
• et-words (neuter) take andet

Since automat is an en-word:

• en anden automat = another machine

If the noun were an et-word, you would use andet instead.

Both patterns can exist in Danish, but they do not behave exactly the same way.

In your sentence:

• ..., så vi går til en anden automat.

Here så is working like a coordinating conjunction, similar to English so, and the clause after it keeps normal main-clause order with the subject before the verb:

• vi går

If Danish begins a main clause with an adverb like så in the sense of then, you can also get inversion:

• Så går vi til en anden automat. = Then we go to another machine.

So the difference is roughly:

• ..., så vi går ... = ..., so we go ...
• Så går vi ... = Then we go ...

Yes, går is present tense of at gå.

• at gå = to go / to walk
• går = go / are going / walk

Danish often uses the present tense where English might also use the present progressive.

So depending on context:

• vi går til en anden automat can mean
  
  • we go to another machine
  • we’re going to another machine

That is completely normal in Danish.

Yes. Automat often means some kind of machine you use automatically or by self-service, especially a vending machine or terminal.

In this context, billetautomat clearly means a ticket machine. Later, when the sentence says en anden automat, Danish avoids repeating the full compound noun, because it is already clear from context that it means another ticket machine.

So the second part is basically shorthand for:

• en anden billetautomat

A fairly literal breakdown would be:

• Billetautomaten = the ticket machine
• ved indgangen = by the entrance
• virker ikke = does not work
• så = so
• vi går = we go / we are going
• til en anden automat = to another machine

So a more literal English version is:

The ticket machine by the entrance does not work, so we go to another machine.

That is already quite close to natural English, which is nice for learners.