HTC MINI 'power button' broken. Need to get data off phone. How?

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May 14, 2016
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The power button on my htc one mini came off, there seems to be no way of switching the phone on at all! I can get it repaired, however they clear all data before repairing and i need important stuff from my phone.
Is it possible at all to switch on this phone without the power button?
It charges fine, when i plug it into my computer it also charges, however no computer i plug it into recognises the actual device to be able to transfer data!
Any ideas?