There is a Surface Pro 4 Battery Replacement guide Units Removing
Disconnect the two display cables and lift the display assembly up and away from the rest of the device. Remove the metal casing of the connecting panel by prying around the edges and then lifting the entire piece once it is loose. Remove screws on a heat sink and then remove the entire heatsink by lifting it out.
Disconnect cables of a motherboard and remove screws. Then remove accessories and motherboard.
Old Battery Removing
Lift battery cables up with the help of hot air gun. Use the pry piece and 530 cleaner to remove the battery and peel the battery up and away.
New Battery Aligning
Paste double-size glue tape onto the new battery and the battery cable before aligning them to the right place of the device.
Install the motherboard, accessories and the heat sink.
Paste double-size glue tape onto the four edges of the display assembly and connect it with the two display cables on the body of the Surface Pro. Dip some B-7000 glue onto the four edges and align the display assembly to the right place. Then clean it.
Power on and test, both screen and battery work normally.
PM - Me - I can tell you how to get your machine replaced if it's still under warranty, which in turn will provide you with a new or "newer", working battery. I won't go blasting off things like this in a public forum, so if your interested, send me a message.