Only Parallels 8 and 9 are compatible with Mavericks. If your version is any of those two try reinstalling Parallels by downloading the latest version of 8 or 9 according to what you have and installing it on top of what you have.
However, if you have an older version of Parallels, I suggest you download the trial of Parallels 9 and use that to retrieve your files before it expires.