It's likely that you get an error because you are running an old version of your software - what you show above probably won't compile:
System.IO.File.Copy(mydatabase & "\PatientenDatabase.accdb", String.Format(backupfolderdestination & "\bac_{0:yyyyMMdd}.backup", Date.Today))
Shouldn't that be DateTime.Today?
System.IO.File.Copy(mydatabase & "\PatientenDatabase.accdb", String.Format(backupfolderdestination & "\bac_{0:yyyyMMdd}.backup", DateTime.Today))
If that doesn't fix it, then use the debugger: put a breakpoint on the first line of the method that throws the exception, and single step through to find out exactly which line is giving the problem and what data it is processing.