I don't own old e-bikes, but I am a physicist with lots of electric trouble shooting experience.
High resistance connections could be sapping your energy. Certainly in 10 years brass, tin plate, lead plate, can oxidize and turn into the insulating oxide. The repair for this is cheap. Disconnect the battery, clean the high current connection surfaces with a wire brush: preferably stainless steel brush to not leave odd metals on the connections. next choice would be a brass wire brush. The pin and socket connections you cant get the brush into , scrape the mating surfaces with a bent tip steel pick.
If that doesn't help, you could contact yuba cycles and see what they want to update your battery and or drive kit. That would be easiest.
If your a DIY type with some electricity background:
If no improvement, I would measure the charged voltage of the battery with a DVM on volts scale. Possibly a 36 v battery will go 38-39-40 v on a charger, but more likely 10 years ago a 24 v battery was installed which would measure 25-26-27 v on a charger.
Then you could build a battery tester. If your battery is 24 v and 10 AH, then it should put out about 10 amps for an hour. You would need a 2.4 ohm load at 240 watts to burn up 10 amps in an hour. You measure the voltage across the resistor and the time it takes the voltage to drop to a discharged state, say 21 v on a 24 v battery. Be sure to do this outside, as LI-Ion batteries are fire hazards. Wear safett glasses. You could solder together 5 of these .47 ohm 50 W resistors to make a 2.4 ohm 250 W load for a 24 v battery.
http://www.newark.com/welwyn/wh50-r47jb006/wirewound-resistor-0-47-ohm-50w/dp/78R5469
for about $6 plus shipping & handling. (newark charges handling for small orders, say <$50)
Using alligator clip leads (also available from distributors) do the experiment, see how long it takes to discharge the battery at 10 A.Warning, these 50W resistors used at 50W will get hot, so bolt to a steel plate or something, lay on concrete drive or sidewalk, and don't touch. Or buy 20 of the .47 ohm, put 10 in series in 2 stacks of 4.7 ohms, then parallel the two stacks to make a 2.4 ohm 500 W resistor that runs cooler.
If the time to get to minimum voltage is under about half an hour on 10 amps, you have a real problem with the battery.
For a 36 v battery you would need a .75 ohm 250 W resistor stack. (or 500 W for safer temperatures).
Or you could just buy a new battery & charger. Technology has changed; make sure the charger matches the battery type.
You could buy a battery of more capacitor than the original but the same voltage. Hangers would have to be fabricated with sheet metal, drill, odd machine screws and nuts, and tin snips.
What I would not do is try to update a 24 system to 36 v or 48 v battery. In case you want the increased wattage and range, just change out the whole wheel, motor, controller, battery & wiring as a system.
Have fun with your bike.
