According to your description, your MacBook can't connect to the battery and can't boot in any mode totally, so if you want to get data off your dead Mac hard drive, what you need to do first is to take off your hard drive from the dead MacBook, put it in a new USB port, and then insert it in a new MacBook.
If the hard drive can work on the new MacBook normally, you can use professional data recovery software to regain your data and remove it from the old hard drive.
iBoysoft Data Recovery for Mac is a powerful tool to help you recover data from USB flash drives, HDDs, SSDs, sd cards easily, quickly, and safely. And it can also help you recover data from an unbootable Mac.
- Download and open iBoysoft Data Recovery for Mac.
- Choose the hard drive and then search for the lost data.
- Preview the data and click Recover.
After that, check if you get back all the data. And you can use Migration Assistant to remove your data into your new MacBook. Likewise, if you have backed up your data in Time Machine, you can use it to get back all your data.