The worst case scenario is that the charging IC has gone bad, let's start replacing the parts that are easiest to replace and cheapest to the hardest and most expensive to replace (being the charging IC last as that is best to be left to a board level phone repair technician to do.)
First of all, did the phone go flat and not turn on again? or did it suddenly just die overnight?
1. Check the charging port for any dust or lint / gunk if the charging cable does not plug in fully. Use a toothpick or something equivalent if there is blockage in there.
2. If the charging port is cleaned or you already tried replacing it then start with replacing / trying another charging dock ribbon cable assembly.
You can get the part from here:
iPhone 5c Lightning Connector and Headphone Jack
Guide to replace the part:
iPhone 5c Lightning Connector Assembly Replacement
3. If that still doesn't work then try replacing the battery:
You can get the part from here:
iPhone 5c Battery
Guide to replace the battery:
iPhone 5c 电池更换
If a known good working battery that is charged can turn on the phone and display working but not phone will not charge even with a new charging dock connector then it is probably the charging IC that has gone to fault.
If it still does not turn on with a known good working battery then you may be looking at a bigger problem like a board issue probably power management ic chip.
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