First try this trick/reset:
Remove the battery.
Plug in the charger (known good charger and cable).
Leave the device plugged in for a minute without the battery installed.
Then with the device still connected, insert the battery, then try to start the phone. Any luck?
If not, may be the charging port you received is defective. Why did you need to replace it in the first place?
Before requesting or ordering a new one though, disconnect the one you just installed, clean the connectors with a cotton swab dipped in IPA 90%+, then reseat and test the phone. This will let you rule out a badly seated cable or dirty connector.
Also make sure the battery is sitting properly. Push it inward a bit, to see if it will make better contact and if you'll be able to start the phone this way.