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I'm sorry to hear about your situation. Absent any voluntary compensation from Mars, there's likely nothing that you could recover (at least that would adequately compensate you). There are a few reasons for this. First of all, there's an issue of proof. You would have the burden to prove that the 3 inch long string was actually in the M&Ms bag. While I have zero reason to doubt that you're telling me the truth (as you're asking about the strength of your case), the jury would have some doubts. When you go to court, you're asking for money, and the jury is going to question whether or not there really was a piece of string in your M&Ms bag. You'd have the burden of proof to prove that it was, and it would really be difficult to prove. Like it or not, the jury is going to look at their own experiences, and unless you have overwhelming proof to the contrary (such as a video of you actually opening the bag that shows the string) they're going to look at their own experiences and realize that they never found a string, and the presumption in their minds would already be against you. Again, I'm not saying that I doubt you. I have zero reason to doubt you here, as you have no reason to be lying to me. But when you're asking a jury to award you monetary damages, they're not going to have that same reaction. They'll be wondering if you're lying to get money from a big corporation with deep pockets.
Next, there's the issue of "damages". You can only recover your actual damages. If you contracted cancer and could prove that you had many years lost as a result of this situation, you could have some significant damages. Having diarrhea, I'm sorry to say, is not a significant hindrance and limitation on life, and while I completely understand that it's embarrassing, such a recovery (if any) would be limited because there's a lack of provable, quantifiable damages.
Finally, there's the issue of "contributory negligence". This is where the other side says that you're at least partially to blame for the situation. In short, Mars would say that while they might have had some culpability in this situation, a "reasonably prudent" person would at least have seen the string and not injested the string in the first place, and that since you did, you were not acting as a reasonably prudent person would. They would phrase this along the lines of absurdity (in that "who would look at a piece of string in a bag of M&M's and say 'well I guess that's something that has to be eaten as well'"). Now I know that this is not what you did, but understand that this is how the Mars lawyer's would frame the situation.
In short, due to lack of proof, damages, and contributory negligence, I think that you would not have a strong case at all against Mars. I certainly think that you should bring it to their attention, and maybe even complain about it online, but if you were to sue them, you would probably lose.
I know this is probably not what you wanted to hear, but it is the law. I hope that clears things up anyway. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (good or better). Thank you, ***** ***** luck to you!