If there was a trouble code set, and the Check Engine Light was on, the factory remote start will not even attempt to crank the engine. The lights may flash, but as soon as it "reads" the code, the computer will shut down the process. If it will not start with the key, but still cranks, there is another issue that will have to be diagnosed.
Check all of the fuses. Check the battery connections. You should be able to hear the fuel pump turn on and run for a second or two when the key is turned to the "run" position before you try to start the engine. These are just the first couple of things I would check.