Jag trodde först att en propp hade gått, men problemet var bara att lampan hade slocknat.

Here propp means a fuse. In everyday Swedish, especially in slightly older or non-technical language, en propp går means that a fuse blows.

So Jag trodde först att en propp hade gått means I first thought a fuse had blown.

Note that propp can mean other things in other contexts, such as a plug or stopper, but here it is clearly about electricity.

This is an idiomatic expression. Swedish often uses gå in expressions where English uses a different verb.

• En propp går = a fuse blows
• literally: a fuse goes

So you should learn gå here as part of the whole expression, not as the usual basic meaning to go.

In Swedish, adverbs like först often come after the finite verb in a main clause.

So:

• Jag trodde först ... = I first thought ...

This is the normal Swedish word order:

• subject + finite verb + adverb

Compare:

• Jag kommer snart. = I’m coming soon.
• Hon såg aldrig filmen. = She never saw the film.

Here först means at first or initially.

So:

• Jag trodde först att ... = At first I thought that ...

Be careful: först can also mean first in a sequence, depending on context. In this sentence, it clearly means initially.

Att means that and introduces a subordinate clause.

So:

• Jag trodde först att en propp hade gått
• I first thought that a fuse had blown

In English, that is often optional:

• I thought that...
• I thought...

In Swedish, att is very common in this kind of sentence and usually sounds more natural than leaving it out.

Because the sentence is referring to something that was believed or had happened before another moment in the past.

• Jag trodde först ... = the thinking happened in the past
• en propp hade gått = the fuse had already blown before that moment
• lampan hade slocknat = the lamp had already gone out before that moment

This is the past perfect:

• hade + supine

Examples:

• hade gått
• hade slocknat

English also uses the past perfect here:

• had blown
• had gone out

Slocknat comes from slockna, which means to go out or to stop burning/shining by itself.

So:

• Lampan hade slocknat = The lamp had gone out

This suggests that the light stopped shining, rather than someone actively turning it off.

Compare:

• Lampan hade slocknat = the lamp went out
• Lampan hade släckts = the lamp had been turned off / extinguished

Related verb:

• släcka = to put out / turn off something
• slockna = to go out on its own

Lampan means the lamp. In this sentence, it refers to a specific lamp that both speaker and listener can identify from the situation.

So:

• lampan = the lamp
• en lampa = a lamp

Since the problem turned out to be with a particular lamp, Swedish uses the definite form lampan.

Bara means only or just.

So:

• problemet var bara att lampan hade slocknat
• the problem was just that the lamp had gone out

It softens the second part and shows that the real explanation was simple, not as serious as a blown fuse.

Because in a main clause, Swedish normally places the finite verb in the second position.

Here the finite verb is var:

• problemet = first element
• var = second element
• bara = comes after the verb

So the normal order is:

• Problemet var bara att ...

This is part of the Swedish V2 rule: the finite verb usually comes second in main clauses.

Yes, in this sentence men works just like but.

It contrasts the first idea with the real explanation:

• I thought the fuse had blown, but the problem was just that the lamp had gone out.

So men is a very straightforward conjunction here.

Yes:

• Jag = I
• trodde = thought
• först = at first / initially
• att = that
• en propp = a fuse
• hade gått = had blown / literally had gone
• men = but
• problemet = the problem
• var bara = was just / was only
• att = that
• lampan = the lamp
• hade slocknat = had gone out

So the structure is:

• I first thought that X had happened, but the problem was only that Y had happened.

Yes, it sounds natural. It is a normal conversational sentence.

A native speaker might also say something very similar like:

• Jag trodde först att en säkring hade gått, men det var bara lampan som hade slocknat.

Here säkring is a more technical/common word for fuse, while propp is also very common in everyday speech, especially in the expression proppen gick.