You have a 36v brushless motor and you believe the battery is good. You suspect the controller is bad. I had a very similar bike with bad controller and fixed it by replacing the controller a couple of days ago. I posted it elsewhere, but here are the gory details again.
I've had good luck with a low end controller on eBay. The ebay controller is from a US vendor who ships quickly; cost is about $17 shipped. It's the same as all the other cheap Chinese 6 FET controllers, except it costs 3 bucks more and ships from the US to you in 2-3 days...
http://www.ebay.com/itm/371239291127?
This controller is very basic. It's plain and simple. You need only to connect power, motor phases, Hall sensors, and throttle connections to run. Docs are weak, so here is what works for me:
For power, connect the power connector heavy red / black pair to positive and negative battery power, and the third small red wire to positive also (it is probably an ignition on signal, which you can choose to switch later). Connect the 5 smaller wires of the Hall sensor connector to their respective colors on your motor. Red is positive, Black ground, and the trio of blue/green/yellow are the sense wires. If you have the same colors just match them, if not come as close as you can. Connect the heavy blue, green and yellow wires to the motor power phases of matching colors, even though that might not be the correct phasing (more later). Connect the 3 throttle wires to the throttle wires of your motor (match red and black power, the third color is the signal). It should now run from throttle input.
If it does not run, probably the phase wires are mixed up. No worries, easy to fix. Connect the two white learn wires together. The motor should start up at a fixed slow speed a few seconds later. That's great. This verifies that your battery, controller, wiring and motor are probably good, but you may have to switch two motor phase wires. If you have the motor running at fixed speed, twist the throttle. The motor may slow down or stop, which tells you the motor phase wires definitely are connected wrong. If so, switch any two motor phase wires. Trust me, this is the easy way to fix the phasing. The motor should now work. Remember to disconnect the learn wires now.
You can now connect the brake wires, if you want the brakes to kill motor power. You should, or you will burn out your motor fighting the brakes. My brakes have switches that close when you pull the brake levers. Test your brake levers switches with a voltmeter to be sure that is how they work. If so, wire both brake switches in parallel and connect to the two controller wires labeled "low level". Verify that the brake levers interrupt motor power when pulled. Ignore the "high level" wire from the controller.
There is no PAS input or speedometer input on this controller, which is fine with me. I like that this is a simple controller that has few things to break, so I don't miss the fancy functions.
Because the controller burned up, I decided to put the new controller up on the seatpost where it can get some cooling airflow. All these Chinese bikes like to bury their controller in a small closed box under the battery. That's like putting your car radiator in your trunk and not giving it airflow. They do it because it's neat and tidy, but I'd rather have reliable and messy. So I moved the controller. You might want to consider why your controller failed and if the reason might be the same.