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Hi, I have removed the battery in the MacBook pro 2013 .. to get to the mouse pad, and now the battery does not work it will not turn on the MacBook it did have around 50% of charge !

Sadly, the battery in this system is glued down! Often you need to replace the battery unit after pulling it free. As the force to pull the battery cells free breaks the internal connections within it and/or damages battery cells case which could lead to a fire!

Does the progress bar get about 60% of the way through before it shuts down? Try booting in Safe Mode ( hold down the Shift key on start up), let us know your results. Have you have any video anomalies like artifacts, mixed colors, any strange video issues?