Hello and welcome to JustAnswer! My name is ***** ***** I will do my very best to assist you today.
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Thanks for your patience.
Please tell me the model of MacBook and current OS your running.
What is your MacBook's serial number please?
You should be able to obtain the serial number on the bottom of the book, or under the battery area.
Let me check and be back shortly.
I could not verify that was the correct sn, but no worries. Let's start with taking out the battery again, and disconnect the AC. Then hold the power button for well over 20 seconds.
Then, reinstall the new battery and hook up the AC again. Wait 20 minutes before attempting to power it on. We want to give the ac a chance to initial the new battery which can take between 10 to 20 minutes.
Then after 20 minutes has passed try hitting the power button to turn it on again and let me know the results.
BTW - I was able to verify the sn finally. MacBook Pro (13-inch Mid 2010), as you are probably aware it is out of warranty. Not that we need it for our use anyways, but I always like to check so that we do not do anything to void a warranty if one exists.
With regard to your new battery, did you buy it from Apple, or is it an aftermarket non apple branded battery?
Ok, no worries. It should be fine. So before this happened, with the old battery still installed, it powered on just fine? If so please tell me the procedure you took to uninstall the old battery and install the new one.
Okay, then let's wait the 20 minutes and see what happens. It might also be a wire or connector has been made loose. We will cross that bridge when or if we get that far.
Okay, lets do the same procedure with the old battery please.
Okay, then what your looking at is a loose connection or dislodged cable most likely. hold on
Are you good with taking things apart farther than just the battery?
Here is what I suggest for now. This will finally tell us if it's hardware related or power related...
Reset SMC of a MacBook Air, MacBook Pro Retina, or MacBook Pro’s with an internal non-removable battery
This is how to reset SMC on most modern Mac laptops, none of which have a removable battery:
Do keep in mind that by resetting the SMC you will lose power specific settings, like the time it takes to sleep a Mac and other customizations to power settings. No big deal, but if you have made many changes to your hardware behavior you will want to adjust stuff like sleep behavior again.
The boot time after resetting a machines SMC can be a bit longer than usual, that is normal.
I am going to also send you a service manual for this MacBook. It may be more info then you need, however you seem to be a person who has no issue digging in and trying things out to try and fix it. Otherwise, if you do not want to do that, then you might be looking at taking it to a Apple store for repairs because if this does not do it, then it is most likely hardware or a cable or connector came loose.
Try it with the new battery and if no dice then have a look at the service manual I'm giving you here, if that is not fruitful, then I am sorry to say that Apple Store here ya come! in any case, I am hopeful, in the event that this is still not working that you can see to it that you accept my answer and rate my service as I did all I could to help, but in the end, it has to be something that was done during the uninstall and reinstall of the battery with a wire or cable or connector. Please let me know what the verdict is.
Thanks in advance.