problem about Airbag Module battery

My battery died. I went to the parts store, but the battery didn't have a screw place on positive side. Knowing I was in over my skills, I went to the dealership with my radio on and no lights illuminating in my dash. The dealership didn't have a proper battery. The solution they presented was change the positive battery cable and use the already purchased battery. Next, they claimed that battery would not hold a charge. The solution they suggested was to purchase a battery from them. I did (and had a hard time returning the other battery). Then, the mechanic drove my car from the shop to the front office and turned the car off. When I got in to leave, my car wouldn't start. As they opened the hood, I saw the replacement cable. The original had a plastic cap; the replacement was just a plain metal one with bolts. The mechanic came and tightened the negative cable. When he started my car, a little smoke came from the negative side. My car started, but the radio didn't work and air bag light was on. Since it was after 5pm, they told me to come back tomorrow. They replaced a fuse and radio worked. They drove the car out to me, but the airbag light was still on. They want $600 to replace the air bag module SRSCM. The module code was due to internal failure. He said it was probably because of low voltage. Fuses blow for overloads, not low voltage, right? What could be the cause of the blown module (improper battery cable, battery connected incorrectly, low voltage, or ??)? Also, should I be made to pay $600 for something that happened to my vehicle while it was in their care?

My battery became too low to start after I used a light and inflator combo set powered by my cigarette lighter while I was changing a flat. It took me about 30 minutes to change my flat. After the boost, I did make a few stops before I got to the shop and turned my car off. When I turned it back on to continue to the shop, neither item had issues at any of the stops. If the damage was done with the boost, why did the radio work on the way there and I not see the airbag light until after the work was done on my car?

Sorry about your troubles. Generally, a surge in the electrical system can cause a problem, however I have not seen this before by simply replacing a battery.
I must say (sadly) that your troubles began before you visited the shop. In addition to coming to them with an electrical problem, based on what you've told me, there is most likely no way that what they did caused an airbag related problem. My initial guess is that whatever killed the 1st battery, did the damage to the radio circuit and the airbag circuit. Something like jumping a car with the cable reversed would do that, but installing a battery, tightening a negative cable and replacing the positive cable shouldn't damage those circuits.
Both of those circuits are 'key on' circuits only, so whatever happened was a result of what happened before the work was done and when the key was already on.
Although you don't tell me what kind of vehicle yo have, you can certainly obtain a good used control unit for far less money. and even replace it yourself (if you feel confident).
Check out my company website pages. We don't sell parts, but can certainly help you in understanding your car better, and provide you with information on where the parts are all located, what the codes mean and if you can clear them yourself. We also have a link to a reputable airbag parts reseller in FLA
There were no recalls for your year, make & model vehicle for the airbag system. There were however 7 other complaints (out of 26 total complaints) surrounding the airbag light just coming on by itself...one with a radio problem such as yours. It seems as though these units do just simply fail and from my experience with Hyundai they are a very sensitive control unit. It does not surprise me that a surge would fry one of these.
The good news is you can replace this yourself with minimum mechanical ability required. It can be bought for as little as $50 from any number of salvage yards. Try this site. I'm sure you can find what you need

www.car-part.com
It's the website all the salvage yards use when they say "Hang on--let me see if my other yard has it". Actually it's an online database of all the salvage yards in America. You can search by part, location or price

Regarding the replacement, the first thing you do is disconnect the battery and wait 10 minutes. Then, the control unit is located under the center console on your vehicle. There are phillips head 4 screws that hold the console in place. Once it is out, there are 4 bolts that hold the control unit in. It's a plug and play unit so it does not need to be reset,. Once installed, reconnect the battery and your light should go out. If you would like step by step pictures of the replacement, email me directly at dgan@airbagsolutions.com & I can send them to you.
I hope this helps you (a little)