I was not able to run it with the dead battery, even plugged in. It would start to boot, but once the OS kicked in with all the graphics, it would die. I managed to get Ubuntu Linux to work on it a little better, but I would not suggest it. It did not work well enough to use, and Ubuntu didn’t have drivers to run the pen or touch screen very well. Ultimately, replacing the battery worked, and I am now enjoying my Surface Pro 4 again!
Thank you for this teardown and instructions! I just finished repairing my Surface Pro 4 after it sat for a year as a brick when the battery died. (I couldn’t get it to reliably boot up - and stay up - with a bad battery, even when it was plugged in.) I purchased all of the suggested equipment but ended up having to use a razor to shave off some of the aluminum case - near the indentation where the speakers are - in order to get the opening pick under the screen. The pictures were very helpful. Mine had a fan attached to the heat sink on the left side of the device, which meant there were a couple more screws to remove, but otherwise, the teardown was spot on.