Create a new, minimal RMarkdown document that includes the sample image.
See if the problem occurs when you try to knit this new RMarkdown document. (if not, that at least helps narrow things down!)
If the problem does occur, then definitely post the contents of your new sample Rmd, and also the output of running the following three commands from the console in your new RStudio Project:
At the same time, you might try seeing if your original file will knit if you set self_contained: false in the YAML header. This doesn't solve the problem if you want self-contained HTML output, but it might be a workaround.
Along with what Andres has said, if you're in a situation where you'll have to insert a image from a code chunk (I can't imagine, though), you can use the knitr::include_graphics function.