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Either the battery is faulty or there is something shorting out in the phone.
If it was a short of some sort the battery would be getting hot due to the sudden discharge.
I would get the battery checked or buy a cheap replacement to test.
Did you do a ROM upgrade without the battery in the phone? if you did this could be your problem as the battery HAS to be in the phone and preferably at 100% charge before and flashing is done. It would be unlikely that the flash process was completed despite what the pc may report.
This leaves three possible problems with your phone,
1, The guy that repaired your phone has introduced a fault. This would be the first thing on my list as you appear to say that the phone was working before the fault was repaired the only problem you had was that you had to use an external battery charger.
2, The battery is faulty and needs to be replaced (possibly caused by either age, a faulty charger unit or a questionable repair)
3, The flashing process was not completed correctly you say them battery was not in the phone when you did the ROM upgrade. I would place the battery or preferably a replacement in the phone and reflash the device.
Personally No1 is the prime suspect for me and as I side note I would have never attempted to flash a device that had a fault without rectifying the fault first. The phone not being able to turn on after an attempted repair can only really point to a bodged repair.