Did you look inside the old battery? It may well be just a bunch of 18650 cells with some electronics in a plastic case. Just desolder the old cells and solder on new ones.
I did the same for my wife's cordless vacuum, and it works better than new, because the new cells are about 2x the capacity of the originals.
Luckily, I do happen to know that stuff, so I used the existing board with brand new 18650 cells. Unfortunately, the board seemed to brick itself when it lost power, so the vacuum kept complaining the battery wasn't kosher.
>This is only good advice if you're good at soldering
I meant soldering onto the pre-welded tabs that come with the new cell (unless you have a spot welder). You don't need much soldering experience for that.
>and know details about cells like which ones have in-built protection.
It's highly unlikely that the individual cells would be protected ones. Manufacturers are not stupid to pay N times the cost of a management circuit.
I don't think you'll ever find a battery pack using cells with integrated low-voltage protection, if that's what you're referring to. All that stuff is managed by the BMS.
What you should be on the look-out for is the cell's operating range, continuous and max power. Personally I use buy VT6's in bulk and never think about any of that.
Lets go with the usual reminder: de-soldering / soldering Li-ion cells can be super dangerous. With a bit too much of heat it can fire or even explode...
I mean, if you want to think I broke it, you're free to. The fact remains that my battery connections were correct, the voltages were right, but the vacuum didn't work with either the battery I made or the new one I bought.
I did the same for my wife's cordless vacuum, and it works better than new, because the new cells are about 2x the capacity of the originals.