System nie działa, więc nie mogę się zalogować.

Because the sentence contains two separate negative ideas:

• System nie działa = The system is not working
• nie mogę się zalogować = I cannot log in

In Polish, each verb that is negated normally gets its own nie. That is why you see it twice.

Więc means so, therefore, or thus.

In this sentence, it connects cause and result:

• System nie działa = cause
• więc nie mogę się zalogować = result

So the whole structure is basically:

• The system isn’t working, so I can’t log in.

It is a very common conjunction in everyday Polish.

Móc is the infinitive, meaning to be able / can.

In the sentence, you need the conjugated form because the subject is I (understood in Polish):

• móc = to be able
• mogę = I can / I am able

So:

• nie mogę = I can’t

This is just the 1st person singular present tense form of móc.

Polish often drops subject pronouns when the verb ending already shows who the subject is.

Here, mogę clearly means I can, so ja is unnecessary.

Compare:

• (Ja) nie mogę się zalogować = I can’t log in

Both are possible, but leaving out ja is more natural unless you want emphasis.

Się is a reflexive particle that is part of many Polish verbs. In this case, zalogować się means to log in.

You should learn it as a whole expression:

• logować się = to log in
• zalogować się = to log in / to have logged in successfully, depending on context

English does not use a reflexive word here, but Polish does. So się is not optional.

This is about aspect, which is very important in Polish verbs.

• logować się = imperfective
• zalogować się = perfective

Very roughly:

• logować się focuses on the process, repetition, or general activity of logging in
• zalogować się focuses on completing the action successfully

After móc / nie móc, Polish often uses the infinitive that fits the intended meaning. Here, nie mogę się zalogować means:

• I can’t manage to log in
• I’m unable to log in successfully

That is why the perfective zalogować się is very natural here.

In Polish, się often appears before or after the verb, but not usually at the very beginning of a clause.

So these are common patterns:

• mogę się zalogować
• nie mogę się zalogować

This placement is natural and standard. You may also sometimes see zalogować się when the infinitive stays together as a dictionary form, but in full sentences się often shifts position.

No. In normal Polish, system is usually written with a lowercase s unless it begins the sentence, as it does here.

So:

• System nie działa.
• Ten system nie działa.

Only the first word of the sentence is capitalized here.

Here nie mogę is followed by an infinitive verb, not a noun, so there is no special noun case issue in this part.

Structure:

• nie mogę
  • infinitive
• nie mogę się zalogować = I can’t log in

This is very common in Polish:

• Nie mogę przyjść. = I can’t come.
• Nie mogę pracować. = I can’t work.

So the sentence is built with a modal verb (móc) plus an infinitive.

In many computer-related contexts, zalogować się covers log in, sign in, and sometimes log on.

So this sentence is very natural for all of those meanings:

• System nie działa, więc nie mogę się zalogować.

Depending on context, Polish speakers may also use similar expressions like:

• nie mogę wejść na konto = I can’t access my account
• nie mogę się zalogować do systemu = I can’t log into the system

But zalogować się is the standard verb for logging in.

It could be. The sentence as given is simply shorter because the context is already clear.

You can say:

• System nie działa, więc nie mogę się zalogować.
  = The system isn’t working, so I can’t log in.

Or more explicitly:

• System nie działa, więc nie mogę się zalogować do systemu.
  = The system isn’t working, so I can’t log into the system.

The shorter version avoids repetition, since system was already mentioned.

For machines, software, and systems, działać is the normal verb for to work / to function.

• System nie działa = The system isn’t working.

Pracować usually means to work in the sense of a person working, or a machine operating in some contexts, but for software/system failure działać is much more natural.

So System nie pracuje would sound odd in most everyday IT contexts.

A rough pronunciation guide is:

• System nie działa, więc nie mogę się zalogować
• approximately: SI-stem nye DJA-wa, vyents nye MO-ge shye za-lo-GO-vatch

A few helpful notes:

• nie sounds roughly like nye
• działa sounds roughly like DJA-wa
• więc sounds like vyents
• mogę has nasal ę, but in normal speech it often sounds close to mogeh / moge
• się sounds roughly like shye
• zalogować has stress on -wać? No—Polish stress is usually on the second-to-last syllable, so here it is za-lo-GO-wać

Polish stress in this whole sentence is regular and predictable in most words.