power on issues with mac air

hello, i have a macbook air 11” 2013 that the battery went dead. i placed the charger on the device and it would not charge. about a year ago i replaced the charging board on this laptop and had success with it after that for awhile. i dont recall letting the battery fully drain though. i recently went to turn on the laptop after it had sat for a long time. i only get a flashing green light on the charger every 12 seconds or so. i reset the pram and smc, disconnected the battery cable from the board and still will not take a charge. if i hold down the power button with the battery cable connected it will turn on with the fan at full speed. if i leave the charger connected and restart, shutdown or boot into safe mode it only takes a press of the button to turn on but fan still running at full speed. if i disconnect the charger at any point the laptop will not turn on until i hold in the power button. oh when i hold in the power button at first the light is off then will go solid green and after about 6-7 seconds it will turn on. is this a bad battery or another faulty charging board? when i login there is no battery percentage showing on the screen so i guess it could be the logic board. i also have turned on the laptop with the battery disconnected with the same results. thank you in advance for any help