Very hard to say because you have a laptop with an unknown history and now an unknown third party battery. Plus there is the matter of whether there was any accidental damage during the repair process since the Logic Board had to be removed and whether all the cables & connectors are properly seated.
Unfortunately the quality of third party Lithium batteries is extremely poor even when purchased from a respected vendor such as OWC or iFixIt.
"Not turning on" can be due to multiple issues especially with these USB-C Mac since there are very few signs of the laptop powering on. Maybe the display backlight is out, or there is no video signal, etc. Even with all original Apple OEM parts, these USB-C Macs are quirky and won't always power on and are a huge pain to troubleshoot.
I take it the laptop never powered on after replacing the battery?
Try an SMC Reset.
When connecting the charger, do you hear the laptop "ding" to indicate it is receiving power?
Try disconnecting the battery....both the flex cable and the T5 BMU screw. Keep in mind without the battery connected, the laptop should power on, but it may take forever to boot since the system will be running at idle speed (800MHz) and could take an hour or all day to actually boot. The purpose is to make sure the laptop powers on and begins to boot. If it does, try re-connecting the battery while the laptop is powered on as it may allow the battery to charge (the battery won't be seen in macOS until you reboot though). Let the battery charge a bit, then try a reboot if possible, otherwise force a power off & try to power on again.
Make sure the battery flex cable is not damaged and is fully seated into the connector (some have a connector on both ends of the flex cable). And make sure the locking lever is closed and the connector is not damaged since that connector is very fragile.
Try using another USB-C port for the charger, especially one on the other side of the laptop. Make sure the charger is connected directly to the laptop and disconnect all other external devices.
Do you have the Touchbar or non-Touchbar model?
