I saw the 'brushes' thing and was thinking it may not be a mistranslation of 'brushless' but instead an Engrish version of what we call 'brushed', which is even worse.
Big points to the OP for trying to do something nice for someone, but I'm afraid it is unlikely you will get this thing to work.
With that said, the controller label does tell us that the battery system is what is known as '36v'. A 36v system has a full charge/discharge range of roughly what you see on the label. Actually the peak is 42v but the label more or less encapsulates the 36v range. Its certainly not 24v (the next step down) and it ain't 48v, whose range is way out of whack with that label, so you need a 36v battery.
What that leaves for you to find is a 36v battery that fits in that space. Your next move is to get a pack with open leads - a red wire and a black wire. Those are easier to find than you might think; especially if you are willing to use a set of nippers to make them bare leads. Then you find the corresponding wires on the bike and make your connection manually with a crimp or a solder. Carefully, and hopefully only if you know what you are doing.
Thats what its going to take to bring this bike back from the dead... assuming the motor still works.
Be advised this is how all those bike shops and apartments in NYC burn down... Well-meaning people doing inexpert work. If you don't have the experience to do this sort of thing, there's no shame in that.
EDIT: It is entirely possible this bike is so old it was meant for use with a lead-acid battery and not li-ion.
