You can flash without AC but most software (particularly windows based ones) won't allow it... However, I don't know if that's your problem...
So you physically replaced the jack in the computer? Because a loose connection would be my first suggestion to check on. If you did and you're 100% sure it's getting a solid connection, can you confirm the actual power supply is correct and working? Not some aftermarket one or anything like that. Or if it's original, could you try another to see if it might not be putting out the correct power.