Just helped a friend fix this exact same issue on his 2004 hyundai santa fe. Replaced the purge control valve - a $39 part, even from the dealer. Had to get our hands dirty, but it took literally one single hour to replace the part. Filled it up immediately afterward and no more starting problems. Part is located directly behind the manifold - top, rear of the engine compartment - just between the engine and the firewall, and you have to remove the big plastic engine cowling/cover (6 small screws hold this down) to get to the valve. (Disconnect battery first...)
Two hoses to disconnect and one elec. connection. Part sits inside a rubber "sleeve" to hold it on a little tab there. Remove from sleeve... put new part in... reconnect to hoses and elec. plug.