Learn Hardcore Hebrew: אין לי סיסמה לרשת הזאת, ולכן אני לא יכולה להתחבר לאינטרנט. - I do not have a password for this network, so I cannot connect to the internet.

Literally, אין לי סיסמה is something like There is no password to me.
So אין is the special word used for there isn’t / I don’t have in this kind of sentence. You would not say אני לא יש לי or אני אין.

What exactly does לי mean?

לי means to me or for me.

It is made from:

ל־ = to, for
־י = me

So:

לי = to me
לך = to you
לו = to him
לה = to her

In possession sentences, Hebrew uses this to someone structure:

יש לי סיסמה = I have a password
אין לי סיסמה = I don’t have a password

Why is it לרשת הזאת, and where did the ה of הרשת go?

This is a very common Hebrew spelling pattern.

The basic phrase is הרשת הזאת = this network.

When the preposition ל־ comes before a noun with ה־ the two combine. So:

ל + הרשת becomes לרשת in normal unpointed writing

So לרשת הזאת means for/to this network.

In pronunciation, this is understood as la-reshet hazot, even though the separate ה is not written.

Why does הזאת come after the noun instead of before it?

In Hebrew, demonstratives like this and that usually come after the noun.

So Hebrew says:

הרשת הזאת = this network
הסיסמה הזאת = this password

That is the normal word order.
English puts this before the noun; Hebrew usually puts הזה / הזאת / האלה after it.

Why is the phrase סיסמה לרשת הזאת using ל־? Why not של?

Here ל־ means something like for:

סיסמה לרשת הזאת = a password for this network

This is natural Hebrew when you mean the password used in connection with something.

If you used של, the meaning would shift more toward ownership:

הסיסמה של הרשת הזאת = the password of this network / this network’s password

Both can make sense, but סיסמה ל... is very natural when talking about login or access credentials.

Why is it אני לא יכולה and not אני לא יכול?

Because the speaker is female.

In Hebrew, יכול changes for gender:

אני יכול = I can, said by a male speaker
אני יכולה = I can, said by a female speaker

So this sentence is being said by a woman or girl.
A male speaker would say:

ולכן אני לא יכול להתחבר לאינטרנט

Is אני necessary here, or could Hebrew leave it out?

Hebrew often drops subject pronouns, but here אני is very natural and helpful.

The form יכולה shows gender and number, but not person as clearly as a fully inflected past or future verb would. Because of that, speakers often include אני for clarity:

ולכן אני לא יכולה... = very natural
ולכן לא יכולה... = possible in some contexts, but less complete on its own

So yes, אני could sometimes be omitted in conversation, but keeping it is clearer and more standard in a full sentence.

How does יכולה work here? Is it a normal verb?

יכול / יכולה means able or can.

In modern Hebrew, it works a lot like the English modal can, even though grammatically it behaves more like an adjective or participle. It is followed by an infinitive:

אני יכולה להתחבר = I can connect / I am able to connect

So in this sentence:

לא יכולה להתחבר = cannot connect

What does להתחבר mean, and why is it followed by ל־?

להתחבר means to connect, to log in, or to join, depending on context.

In a technology sentence like this, it usually means to connect or to log in.

It normally takes the preposition ל־:

להתחבר לרשת = to connect to a network
להתחבר לאינטרנט = to connect to the internet

So the ל־ before אינטרנט is required by the verb.

Also, English often says the internet, but in Hebrew אינטרנט is very often used without ה־, especially in everyday speech.

What does ולכן mean? Is it different from אז?

ולכן means and therefore, so, or that’s why.

It is made of:

ו־ = and
לכן = therefore

So it links the two parts logically:

no password
therefore cannot connect

Compared with אז, ולכן sounds a bit more explicit and slightly more formal or written.
אז is often more conversational, while ולכן clearly marks cause and result.