It can't if it isn't plugged in.
Anyway, I thought the problem was that pressing the button overrides turning wireless off in the GUI. It would be quite an amazing router that could turn its wireless on for your son if it is not powered up, has the wireless turned off in the GUI and he can't get at the button.
How long is this film he's watching?

How old is he?
How does it stop you sleeping?
There must be some solution!
My broadband basic info/help site - www.robertos.me.uk |
Domains,website and mail hosting - Tsohost.
Connection - Plusnet UnLim Fibre (FTTC). Sync ~ 53.4/16.8Mbps @ 600m. -
BQM
"Where talent is a dwarf, self-esteem is a giant." - Jean-Antoine Petit-Senn.
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Allergy information: This post was manufactured in an environment where nuts are present. It may include traces of understatement, litotes and humour.