The engine light will come on if there is a percived fault relatig to the engine, it doesn't just cover the exhaust.
You need to get a scanner to read the ECU to get the code to see what the fault code is, there are hundreds.
http://www.troublecodes.net/OBD2/ gives an insight -
P 0 1 0 1
1 2 3 4 5
1st digit
P = powertrain
B = Body
C = Chassis
2nd digit
0 = Standard
1 = Manufacturer specific
3rd digit
1 = Emission management
2 = Injector circuit
3 = Ignition
4 = Auxiliary emission
5 = Vehicle speed & idle control
6 = Computer & output circuit
7 = Transmission
4th and 5th digit give the actual fault.