El electricista dijo que el cable de la lámpara estaba viejo, pero que la despensa seguía en buen estado.

This is very natural in Spanish. The second que connects the second reported idea back to dijo.

So the structure is:

El electricista dijo que X, pero que Y.
= The electrician said that X, but that Y.

Repeating que makes it clear that both parts are what he said. In English, we often drop the second that, but Spanish commonly keeps it.

Because both verbs describe states or conditions rather than completed actions.

• estaba viejo = was old
• seguía en buen estado = was still in good condition / remained in good condition

The imperfect is very common for background description and ongoing situations in the past. The sentence is reporting what the condition of the cable and the pantry was at that time.

Seguir adds the idea of continuing or still being.

• estaba en buen estado = it was in good condition
• seguía en buen estado = it was still in good condition / it remained in good condition

So seguía creates a contrast with the first part:

• the cable was old,
• but the pantry still remained in good condition.

Because viejo agrees with cable, not with lámpara.

The noun being described is:

• el cable → masculine singular

So the adjective must also be masculine singular:

• viejo

de la lámpara is just telling you which cable it is: the cable of the lamp.

Spanish often uses de to show possession or connection.

• el cable de la lámpara = the lamp’s cable / the cable of the lamp

This is a very common structure in Spanish. English often prefers 's or noun compounds, but Spanish usually uses de.

It is a very common expression meaning in good condition.

You can use it for many things:

• un coche en buen estado = a car in good condition
• un edificio en buen estado = a building in good condition
• una despensa en buen estado = a pantry in good condition

The opposite is en mal estado = in bad condition.

Because dijo que is introducing a reported statement, so Spanish normally uses the indicative, not the subjunctive.

• dijo que el cable estaba viejo = he said the cable was old

The subjunctive would appear in a different kind of sentence, for example after a command or wish:

• dijo que cambiaran el cable = he said they should change the cable

So here, since it is just reported information, estaba and seguía are correct.

Spanish uses definite articles more often than English does.

Here, the sentence is talking about specific, identifiable things:

• the electrician
• the cable
• the lamp
• the pantry

That is why the articles sound natural. In English, we sometimes leave articles out more easily, but Spanish usually keeps them.

In Spain, despensa usually means a pantry, larder, or sometimes a storage cupboard/room where food and household supplies are kept.

Depending on the home, it could be:

• a small pantry room,
• a cupboard,
• or a storage area for food.

So in Spain Spanish, it is a normal everyday household word.

It can mean both, depending on context.

For objects, viejo often suggests that something is not just old in age, but also aged, worn, or deteriorated.

So in this sentence, el cable... estaba viejo probably implies more than just age. It suggests the cable may have been old enough to be a concern.

Sometimes yes, but keeping it is very normal and often better style here.

Compare:

• El electricista dijo que el cable de la lámpara estaba viejo, pero que la despensa seguía en buen estado.
• El electricista dijo que el cable de la lámpara estaba viejo, pero la despensa seguía en buen estado.

Both can be understood, but the version with the second que more clearly shows that both clauses belong to what the electrician said. It sounds especially natural in careful, connected speech.