ABS Working but no TCS
 

My TCS is not working for some reason. Granted the car is now 14 years old and the TCS button is in-op. ABS is good but any ideas? Also, I have an I30T and I should have limited slip diff as standard equip. Unsure if it is working or how would I confirm I have it? One wheel on ice and the other on pavement and have someone floor it? Thoughts are appreciated.