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)]”
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”
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.