Turning power back on during the prayer after a power outage

The worshipper should avoid making movements that have
nothing to do with prayer whilst he is praying, especially if there is no
need to do that whilst he is praying, because that is part of establishing
prayer properly as we have been commanded to do. Allaah says
(interpretation of the meaning): 

“Guard strictly (five
obligatory) As‑Salawaat (the prayers) especially the middle Salaah (i.e. the
best prayer ‑ ‘Asr). And stand before Allaah with obedience [and do not
speak to others during the Salaah (prayers)]”

[al-Baqarah 2:238] 

Shaykh Ibn Sa’di (may Allaah have mercy on him) said in his
Tafseer: i.e., with humility and proper focus. 

And Allaah says (interpretation of the meaning): 

“Successful indeed are the believers.

2. Those who offer their
Salaah (prayers) with all solemnity and full submissiveness”

[al-Mu’minoon 23:1-2] 

With regard to what you mention about one of the worshippers
stepping forward to turn on the microphone whilst he is praying, this
movement of his does not invalidate the prayer. If there was a need to turn
on the microphone during the prayer, such as if the congregation was large
and they could not all hear the imam’s voice, then he did well by doing
that. 

But if there was no need to turn on the microphone during the
prayer, then he did a makrooh action, but his prayer is not invalidated,
because such actions are regarded as small movements which do not invalidate
the prayer. 

For more information on the rulings on moving during the
prayer, please see question no.
12683. 

But we should point out here that amplifiers should not be
used outside the mosque as many people do nowadays, because that disturbs
worshippers in other mosques or people who are praying in their homes, such
as women and those who are exempted from praying in the mosque. Please see
question no. 35821. 

And Allaah is the Source of strength.