steering wheel shaking and check engine light stays on on 1996 Nissan Sentra

Recently the steering wheel started shaking at low speed. What could be causing this?
Also, the "check engine" light is staying on, why?

Asked by for the 1996 Nissan Sentra
If the shaking is while braking you have one or more warped brake rotors. If, not then perhaps a front tire is out of balance, damaged, or a wheel is bent. As for the Check Engine Light, please review the following RepairPal article -