Traction light on, car won't excellerate

This could get lengthy.

My daughter was driving her car the other day. (The weather was rainy.) She was about twenty minutes into her journey and the "check engine soon", "Traction, " and "ABS" lights all came on. (She didn't notice any sounds or feelings that were different at the time, but she's not observant.)

So, we take the car to our mechanic (which BTW, no lights came on the next time she started the car). He put it on the computer and everything was fine. He drove it, and checked somethings (not sure what but I'm sure it was easy to check things.) No lights, no indication of any problems on the computer. He did say that her front tires were almost bald.

So, the next time she drives the car to college (30 minute drive) and she has no problem. However, on the way home, she stopped at a light and when she tried to accelerate the car wouldn't accelerate. (She said it felt like her old vehicle did when the timing chain broke. Without and noise or thud. Just the not accelerating.) She pulled off the road, shut the car off, turned the car back on, and there was not any light. So she tried to drive and had no problem the rest of the way home. (She had driven through a wet area, but it was not raining or wet when the car started acting up.)

We can't afford hit and miss repairs (which my mechanic would not do, but he did not find anything wrong.) My question is, obviously, "What is wrong?" But, I am wondering if this could all be the result of the low tread on the front tires and wet roads?

Thanks.