2002 Buick Century ABS problem

I have had a service vehicle soon light, abs light and trac off light on for a while. It occasionally would go off for a period of time (sometimes a couple of days or more) recently the light would come on shortly after starting the vehicle and driving a little ways, and then it would stay on until the car was turned off, then repeat the problem. I went to a local auto parts store and had them run the diagnostics, they showed a code for the front left wheel speed sensor. I bought and replaced the front left hub assembly which has the sensor in it. This did not fix the problem and I started to notice an intermittent hum coming from that wheel. The hum was not constant and seemed to be tied to the abs somehow. (It sounded like the ABS was trying to engage, I could feel the vibration on the floor of the car, the brakes have never engaged though, just the hum) This hum happens with all dash light off and then eventually the ABS indicator lights come on the dash. When the lights come on the dash the ABS should be disabled? However the hum is still occurring intermittently. I checked the connection and the wires leading to the wheel speed sensor. I found a busted blue wire (wire was pretty oxidized from water contacting it) and soldered the connection then checked the ohms with a volt meter, the connection seemed good. Any suggestions? Could the EBCM be faulty or the replacement hub assembly/wheel speed sensor. Also is there any way to check the wire back to the brake control module. I'm not sure what the sensor/wire's should ohm out at. I would prefer not to take it to the dealership and get cleaned out.