Engine Cooling problem
2004 Mazda 3 Automatic 60000 miles

i have a 04 mazda 3 and the engine fan won't shut off and is draining the battery. I am not sure what is wrong with it. at first the car would not turn over at all and i thought it was the starter. now it starts up but drains the battery. Someone told me it could be a relay switch. I am not sure what it is but would take any suggestions.