The power steering light comes on and the wheel grips a little. The light does not stay on and I am told that only a dealership can tell you what the problem is. I have a 2005 chevy cobalt.

The power steering warning light coming on in your car is bound to make you worried, especially as it tends to coincide with a total loss of power steering, making it much harder for you to steer your vehicle.
If you've ever driven a car with manual steering, you know how hard it can be. For vehicles with hydraulic power steering, the most common reason for the power steering warning light is that the fluid level is low. This is often caused by a leak in one of the hoses.
If you're driving along and you notice your power steering light come on which looks like a steering wheel with an exclamation mark next to it- you should park your car in a safe place as soon as you can, taking extra care as you'll be struggling a little with much heavier steering.
Open your bonnet and locate your steering wheel fluid reservoir. This may have an image of a steering wheel on the cap. If not, you may need to consult your owner's handbook to help you find where it is.

well all the lights should come on when you start it, it is the system is telling you all is ok, now if it stays on then sorry to say you have to take it to a dealership to have it looked at

I had the same problem. The steering wheel controls are very easy to pop off with a small thin screwdriver. Once they are loose just unplug them. Order new ones from your local Chevy dealership. They weren't very expensive. If I remember correctly they were only about $35 each. Just make sure to get the correct color to match your interior.

Take it to the Dealership have them check it.

The same thing happed to my 06 cobalt. The thing is that the DUMB A** at GM made the whole power steering electrical. Your going to have to change the the little computer that is located right under the steering wheel. if you go to the dealership they are going to RIP YOU OFF. What i did was i got the part at a GM junk yard, all it cost me was $200. your going to have to take the whole steering wheel of and change it. I hope i helped. GM needs to do a recall b4 someone God forbid, dies form this in an accident.
I still do like my cobalt thought lol

wheel bearing

i had a simular problem it was the abs sensor on one of the rear wheels 79.00 part.The wire plugs in under the seat and passes through the floor could be the connection also.

I had the same problem in a way. My airbag light would come on and then go off. The airbag connections in the steering wheel got stuck somehow. It only can rotate lke 3 and 1/2 times and over the years mine just got stuck. (my yukon has over 200000 miles) All i did was press on the horn and wiggle the horn cover for about 20 seconds. I havent had a problem since.

I took my car into the dealership on friday 02-13-09 only to find out my steering column needs to be replaced the motor is shorting out for the power steering ~ certain models of malibu's 2005 yr if your vin falls between 5F100001 - 5F250216 call Chevrolet they have a Technical Service Bulletin # 07126 - SPECIAL COVERAGE ADJUSTMENT - LOSS OF POWER STEERING ASSIST - 7 yrs or 70,000 miles regardless of ownership - they will cover the cost of the repair ~ Chevrolet 1-800-630-2438 or
1-800-833-2438 - They saved me from having to pay out of pocket !!!

Your power steering pump is locked up.