If your case in in Brunswick, there is good reason that lawyers turn it down. In the entire history of Brunswick all the way back to colonial days, apparently there has never been a jury verdict in favor of a plaintiff in a medical malpractice case. One local lawyer who incurred the wrath of the local medical community was blacklisted so that no local physicians would even treat his children. Moreover, at least 80% of all medical malpractice cases that go to trial statewide in Georgia are won by the defense. Since medical malpractice cases are always expensive, difficult and time consuming, the case has to be very clear and extremely catastrophic to be worth pursuing. I'm not sure what you are referring to as a "third party" unless it is a "third party administrator" who manages claims. However, I am absolutely confident that they have no intention of doing anything that you would consider fair.
If you are not willing to hire a medical malpractice attorney on a contingency at the full rate, you may want to consider trying to get help with valuation either at an hourly rate or some type of reduced contingency. It would be impossible for an attorney to guide you through the process in response to your post. It's obvious that an attorney needs to review all of the available information and advise you accordingly.
The hospital risk management may be willing to pitch a few thousand dollars to you, depending of course on the nature of your injury & expenses. They are asking for the medical charges so they can justify this sort of payment to you. Of course, they may very well later tell you that they decline to make any offer. If you take money from the hospital at this point, you are likely forever barred from suing them in the future should you later get a lawyer.
Malpractice cases are very expensive to pursue. That doesn't change just because you have a witness to the incident. Medical experts must be hired, depositions taken, court reporters paid, videographers paid, court filings incurred, etc. These cases cost tens of thousands of dollars to litigate. If a reasonable settlement value of your case is, say, $10,000...it wouldn't make economic sense to lawyer up and spend $30,000 just to get a $10,000 settlement. This may explain why your last attorney bowed out.
I will second the other posters comments that medical malpractice cases are extremely expensive and complex. Thanks to many of the tort reforms that have been enacted, claims for medical malpractice that involve non-catastrophic injuries are very difficult for injury attorneys to take on.
I would suggest you continue to call around to more injury attorneys who do medical malpractice work. It is difficult to give you any real evaluation of the case based on an internet post, but the reality is that bargaining with a hospital on your own is no picnic. After you resolve your case, either through representation or on your own, I would suggest calling your local congressman and asking him/her to vote against tort reform legislation that prevents many attorneys from being able to help people legitimately injured at the hands of a negligent doctor, nurse, or other medical provider.
Sign up to receive a 3-part series of useful information and advice about personal injury law.