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If the power switch truly needs repairing (and it certainly sounds like it), and given the camera being obviously out of warranty coverage, I can say that this repair company:
You will need to contact a repair location directly, to get an estimate for this sort of work.
There is actually only one repair location for FujiFilm themselves in the USA, it is in New Jersey. See this page:
The regular way to get an estimate from them, is to mail in this form:
and they will mail you back an estimate.
Other sites (not FujiFilm) will give you an estimate of repair if you contact them:
So there is no direct quote source directly available, unfortunately... unless you have local shops to ask.
And with your locality info, I will inform you of listings for those.
And, for a power switch replacement, which is not at all a major repair, your price for the repair is not likely to be large.