phone wont turn on unless plugged battery was replaced with orginal

so my screen was broken and i went to phone shop to get it replaced i replaced it however when i got back my phone was not turning on so i kept it on charge and and it turned on and when i took it off the charger it would work for a bit then turn off. initially i though it was the battery and charging port because it was old so i decided to go to the shop the next day and get it fixed. so they replaced my battery and charging port and when i got home it was still turning off when it was not plugged in and refuses to turn on when it isnt plugged in. i have reseted it and still no luck