You will see voltage on both sides even if the coil goes bad. I don't remember 100% but typically there is a diode with that circuit that can go bad. Most likely it is a bad contactor coil if you have battery voltage on both sides and the contactor does not close. I may be remembering wrong but if the contactor is trying to open, the resistance of the coil should be around 28.8 ohms. I'd recommend replacing the whole contactor assembly.