electric problem

I have a 1995 cavalier with high miles a problem arose this afternoon when starting, it turned over very hard like the battery was low but when I checked the battery had full charge,while running the brake light, seatbelt light and ABS light would flash on and off and after awhile the car would shut off, after sitting it would start again but would start hard and do the same thing a desribed, could it possibly have to do with the starter or should I look elsewhere