Why does my check engine light come on? on 2000 Buick Century

I took my car to DEQ, but it failed? I'm not sure if it is either my fuel pump or the fuel filter

It failed because your check engine light is on. Have it checked for free at your local Autozone and they'll give you good place to start. Your receipt from DEQ should already have code written on it (under trouble codes starting with "P"). Id go to Autozone and have them print you the code or codes and go from there. Could be very simple problem. If you have a vehicle 1996 or newer that has check engine light on don't even bother to take for emissions test- will fail everytime. Have checked whenever it comes on and do everything you can to keep light off. In the end it'll save you gas!