Well then, you appear to have purchased a defective camera.
I advise you to contact Canon USA, at 1-800-OK-CANON, and with proof of purchase date in hand, require of them a bit of warranty servicing on the camera, for the defect of being incapable of LIVE Mode (for whatever reason - perhaps a sensor is and has been defective, perhaps this, perhaps that...) and being within 1 year of purchase date and therefore covered by Canon's default 1 year warranty on their products.
Also you have cared for the camera carefully, and so have not voided its warranty.
And you have also tried a settings reset, and you have read the manual (and you've had me to advise you also.)
Good luck with it - Canon's warranty repair service does get rather high marks in reviews, so turnaround time should be fairly brief.
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