Traction control turning on randomly

Hi, since I came up from Arizona to Wisconsin I have had trouble with the traction control kicking in randomly. I will be driving whether the ground is dry or has snow and ice and all of a sudden the traction control light comes on and the engine's power is cut down to like twenty or thirty mph. The suggestion in the book is to put it in L. This does not work. Then the check engine light comes on as well. The next suggestion was to click EB one click and then drive and it should shut off. However that does not work. There is no traction control button in this car to shut it off. So after it went on the other day I kept driving then all of a sudden it kicks off and I can drive it just fine. This has happened twice. Also when the traction control kicks on the speedometer does not work. And the temperature display for outside temperature does not work. If I continue to drive it and it decides to kick off the speedometer and other gauges start working too. The other day I could not get the traction control to kick off. Disconnected battery and all. As this had worked a time or two before. Anyhow I trailered it over to my cousins shop. He tested my battery with tester said it was bad. Bought a new battery. His friend was having trouble with lights on the dash coming on etc. And buying a new battery solved his cars issue. So we left with new battery. Drove thirty five miles and the traction control light came back on. Had to turn around and take it back to my cousins. Halfway there it kicked off and I was able to drive normal the rest of the way. My cousin is a little perplexed and does not understand what is going on with it. Please if anyone knows how to fix this issue I would sure appreciate it. Thank you, Sue