The question is not whether you can sue...of course you can...the real question is whether you have sufficient evidence to prevail. If indeed you have evidence that you became ill due to food poisoning as a result of consuming food at Denny's, you may indeed have a good case.
I suggest you consult with competent counsel and discuss your evidence and options.
Food poisoning cases are particularly difficult. The difficulty is not in showing that you ate at the restaurant, but that the food eaten there is what made you sick AND that you have some permanent injury. The value of personal injury claims is if you have a permanent injury. A problem which you have for a limited period of time and then gets better, is worth a limited dollar amount. You can certainly provide your medical bills to the restaurant and see if they are willing to pay something related to the bills themselves. Seek the assistance of an attorney who has handled this type of claim in the past. I have filed these types of cases and none of them proceeded to trial, they were all settled.
The answers given are limited to the facts as given and presumed by the answer itself. Without seeing actual written documentation or having a conference to more fully explore the issues, this short answer has only limited application. Make sure to seek legal counsel and provide all documentation to get assistance in making informed legal choices. Bstein@dcfsz.com, 305 377 1505