2002 Chevy Cavalier ABS light coming on and accessories not

Had issue with car not running that I thought was my starter switch. Changed it out and car still wouldnt start. Turns out it was just tons of corrosion on battery cable. Put on new cables and car started right up. Now, security and service light goes on and off but I think the system just needs to be reset, so, if anyone knows how to do that, please let me know. The real problem though is Im having accessory issues. When the headlights are on, they and console are very dim. Also, when I step on the brakes, the ABS light comes on, the lights dim more, the a.c. stops pumping cold air and all of my gauges lose power and go down. When I take my foot off the brake, everything goes back to normal. Any suggestions? Also, I notices when I was attaching the new battery cable to the starter that there was another decently thick cable attached to the same terminal that leads up into a harness that has serious corrosion on it. Any chance this wire goes to my accessories?
Thanks