These cases are difficult, and without a serious injury, it probably wouldn't be worth the time and money, but you may search Avvo for a personal injury lawyer in your state and see if the lawyer would take the case on.
Philadelphia Personal Injury Lawyer. www.InjuryLawyerPhiladelphia.com
Maybe I don't understand your question, but if I do, the answer is, "No, you cannot sue a manufacturer for damage to the vehicle." You can, however, sue the manufacturer for damage to your body (i.e., bodily injury) that was caused as a result of the vehicle's airbag failing to properly deploy.
A cautionary note: these cases are extremely tough and it will be very hard to find an attorney willing to handle the case unless (1) you have some meaningful bodily injury and (2) you can show convincingly that an adequately maintained air bag failed to deploy properly (which means you will need the vehicle in the untouched condition so that the airbag can be examined by one or more experts).
Hope that helps you.
You can sue the manufacturer, but that probably would not be a wise idea. Airbags do not deploy until a certain amount of force is detected by the car's sensors, and that force may have been insufficient to trigger deployment here. The fact that you hit your head on the steering wheel suggests that you may not have been using other restraints available in your vehicle, and that will be used as a defense against you. The black box may have information relating to your seat belt use.
If you do not believe you were injured, you have little or no damages to recover, so the expense of litigation likely will result in a net loss to you. If you did hit your head, you should see a medical professional, even if you do not believe you were injured.
Your claim is probably governed by one or more limitations periods. This means that you must take certain actions within a certain period of time to preserve all of your rights. The limitations period can be very short. I encourage you to speak with a lawyer who handles medical negligence cases in your area as soon as possible. I would be happy to help you find someone
You cannot sue the auto company for damage to your vehicle (at least not successfully), because the failure of the airbag to deploy did not lead to the damage to your vehicle.
With respect to banging your head on the wheel, you would have to prove the airbag should have deployed. This appears to be a low-speed accident where the airbag was not supposed to deploy. Therefore, I don't think you could win that case. Good Luck.
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