1984 Mustang trouble

my car was running fine yesterday, but when i woke up this morning it wouldn't turn on. it sounds like a grinding sound coming from the starter relay right next to the battery. the lights dim in my car when i try to start it and it just has a grinding type sound. i replaced my starter and the relay today, not because of this but because it was needed but it still does the same thing. i'm not sure if it's a wiring issue or what. on the top i have the positive cable, the fusible link and the starter wire, on the bottom i have the starter motor cable and on the s i have the ignition wire that slips right on. any and all info is appreciated i gotta get the car running again to get to work!! thanks for the help!!!