2005 Cavalier fan motor not working

I have a 2005 Cevy Cavalier with 94000 miles. It has a 2.2 flex fuel engine and there are no sounds or leaks at the current time. Within the last 2 weeks I have had to replace the alternator and then the battery. Two days after I replaced the battery the radiator fan stopped working and my car now overheats. I have replaced the relay and fuse at the top of the engine and I am able to jump start the fan motor off the battery. When I spoke with Chevy they said that there is another relay and a switch but would not tell me where. I just spent $350 on the car and they want me to bring it in to them for a diagnostic at $80 and said that the repairs could cost another $200. Could you please give me some suggestions that I could try on my own before I have to pay $200 to let them plug in a $16 relay or switch.