Hi, I used to own a Gwiz. I had an 07 AC version.
You say the batteries were in a bad state when you got it and you have managed to nurse them back to health? Do you know the full pack voltage after charging? It should be in the region of 50 volts. what might be happening is that the batteries are in such an un healthy state that as soon as the electronics power up the voltage plummets to below the voltage cut off for the controller - and this is why the car is just not moving.
Your best bet is to visit here http://gwiz.myfastforum.org/
This is a great site for GWIZ owners and there is alot of information to be read.
Try and get hold of the BMS software - this does require a computer with a serial port - but it will allow you to monitor each individual battery so you can see what it's voltage is.