I'm not certain I understand...
Your post states that you are not backing up any remote machines but the server names you reference in the errors indicate MYSERVER and MYSERVER01. So I'm unsure if you substituted generic names for your real server names and made a mistake when transposing the errors or if those are the real server names which indicate a possible attempt at a remote backup.
In either case, if you are only running a local backup...create a new backup job, do not use a previously created selection list, backup only one file (boot.ini). When that backup runs does the same error occur?
If it doesn't then I would suggest that there is a problem with your current selection list or lists. Most likely the quickest way to resolve the problem will be to simply create a new selection list.