Q: Having problems with ABS on my car

My car is making ABS activation noises when I drive between 5 to 15 MPH. It started last year during a snow storm when I had to slam the brakes pretty hard. Now whenever I apply the brakes while moving 15+mph, as the speedometer dips below 15, I can feel the ABS system activating through my brake pedal and can hear the car making a 'grrrrrrr' noise. When the speedometer drops below 5mph, the sound goes away and it feels like regular braking. I brought the car to my mechanic, and he isn't getting any error codes. He has checked continuance through the wires and they're good. The computer says that it's receiving signal. We replaced the wheel sensors and it's still doing the same thing. The mechanic thinks that it might be a computer issue, and he's willing to replace the computer, but it's going to cost about $600 for everything. He's not giving me any promises though, so I said I'd get a second opinion before continuing. The mechanic said that there is no resistance drop on the wires, but that the signal itself is about half of what it should be on the rear passenger side wheel. So, when all the other wheels register 10 mph, that one registers 0mph. Around 10 mph is when I start to hear the groaning of the ABS. Other than that the ABS is just fine. Any ideas?