https://www.ebay.com/itm/Repair-Part-For-Sony-DSC-HX300-DSC-HX400-Battery-Cover-Battery-Door-New-original-/151967487502 here's the part. is it broken Beyond repair? if so it's easy to do.
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=== Update (04/13/2018) ===
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there's not much information on how to fix it. try to bring it to a local electronic repair shop. sorry for the late response
https://www.ebay.com/itm/Repair-Part-For-Sony-DSC-HX300-DSC-HX400-Battery-Cover-Battery-Door-New-original-/151967487502 here's the part. is it broken Beyond repair? if so it's easy to do.