Quando eu perdi a chave, não consegui trancar o carro nem destrancar o portão.

Yes. In Portuguese, subject pronouns are often omitted because the verb ending already shows who the subject is.

So Quando perdi a chave... is also completely natural.

Here, eu is included for one of these common reasons:

• clarity
• emphasis
• rhythm/style

In this sentence, eu is not required, but it sounds perfectly normal.

Perdi is the preterite form, used for a completed event: losing the key happened at a specific moment.

• Quando eu perdi a chave... = when I lost the key

If you used perdia, that would be the imperfect, which usually suggests:

• ongoing/repeated action in the past
• background description
• something habitual

So Quando eu perdia a chave... would sound odd here, almost like whenever I used to lose the key.

This sentence needs perdi because it refers to one completed event.

Both can sometimes be translated as could, but they are not always used the same way.

• não consegui = I didn’t manage to / I was unable to
• não pude = I couldn’t / I was not able to / I was not allowed to, depending on context

In this sentence, não consegui emphasizes the failure to accomplish the action. That fits very well because the lost key prevented the speaker from doing those things.

So:

• não consegui trancar o carro = I couldn’t manage to lock the car

You might hear não pude in some contexts, but não consegui is especially natural when the idea is I tried or needed to do it, but I couldn’t.

Portuguese nouns have grammatical gender.

• chave is feminine → a chave
• carro is masculine → o carro
• portão is masculine → o portão

The articles must match the gender of the noun:

• a / uma for feminine singular
• o / um for masculine singular

This gender is grammatical, so it does not necessarily reflect anything logical in English. You simply learn each noun with its article.

Nem means nor / not even / and not depending on the structure.

In this sentence:

• não consegui trancar o carro nem destrancar o portão

the nem connects two things the speaker could not do:

1. trancar o carro
2. destrancar o portão

So it works like nor or or even after a negative statement:

• I couldn’t lock the car nor unlock the gate
• more natural English: I couldn’t lock the car or unlock the gate

A useful pattern is:

• não... nem...
• not... nor...

Example:

• Não comprei pão nem leite.
• I didn’t buy bread or milk.

They are opposites.

• trancar = to lock
• destrancar = to unlock

The prefix des- often gives the idea of undoing or reversing something:

• ligar = turn on
• desligar = turn off

So:

• trancar o carro = lock the car
• destrancar o portão = unlock the gate

In daily Brazilian Portuguese, abrir o carro can sometimes be used informally in situations where English would say unlock the car, but destrancar is the more precise verb here.

They are different things.

• porta = door
• portão = gate, large door, entrance gate

Portão usually refers to:

• a front gate
• a garage gate
• a large metal or wooden entry gate

The ending -ão here is part of the noun itself. It is not simply a version of porta. They are separate words.

So if the sentence is about entering a property through a gate, portão is exactly the right word.

Because in Portuguese, standard negation usually puts não directly before the verb.

• não consegui = I did not manage / I couldn’t

This is the normal pattern:

• não sei = I don’t know
• não fui = I didn’t go
• não tenho = I don’t have

So não consegui is just standard word order for a negative verb phrase.

Because after conseguir, Portuguese commonly uses another verb in the infinitive.

Pattern:

• conseguir + infinitive

Examples:

• Consegui abrir a porta. = I managed to open the door.
• Não consegui dormir. = I couldn’t sleep.
• Ela conseguiu terminar o trabalho. = She managed to finish the work.

So in your sentence:

• não consegui trancar o carro nem destrancar o portão

both verbs stay in the infinitive because they depend on consegui.

Grammatically, ou would change the nuance.

• nem links two things that are both included under the negative idea
• ou can sound more like a choice or alternative

So:

• não consegui trancar o carro nem destrancar o portão = I couldn’t do either of those two things

This is the most natural choice.

Using ou after a negative is sometimes possible, but here nem is better because it clearly joins two failed actions under the same negative statement.

Yes. It presents a clear past sequence:

1. Quando eu perdi a chave — the key was lost
2. não consegui trancar o carro nem destrancar o portão — as a result, the speaker could not do those actions

Both main verbs are in the preterite:

• perdi
• consegui

That gives the sentence a very concrete, completed past-event feel, which is typical in narration.

The sentence is already natural and compact. Portuguese does not need to repeat with the key or because of that.

The logic is understood:

• if you lost the key,
• you could not lock the car
• and you could not unlock the gate

That kind of cause-and-effect is often left implicit in Portuguese, just as it is in English.

So the sentence sounds efficient and natural as it is.