car will not pass New York State inspection

miles in the last four years . the battery died and was replaced at a caddy repair shop.the check engine lite came on when i brought the car in for an inspection, they replaced a O2 senser and told me to drive the car . i have now driven this car over 4000 mile driven in the last 4 yrs. battery was replaced 2 yrs. ago. new battery was recharged and has not been a problem , no check engine lite was on when i brought it in --- the lite came on and they replaced an O2 sensor, but did not pass inspection. the check engine lite was not on. i was told to drive the car -- i have now driven 400 miles, taken the car back every 100 mile to have checked -- and am being told to keep driving the car. the reggy is now up and i cannot continue to drive in circles.