Solution:
I updated logback from version 1.1.9 to 1.2.3. When I deleted the old jar files and included the new jar files (jcl-over-slf4j 1.7.25, jul-to-slf4j 1.7.25, log4j-over-slf4j 1.7.25, slf4j-api 1.7.25, logback-classic 1.2.3, logback-core 1.2.3), I got 649 times the error "Logger cannot be resolved to a type". I fixed this by opening the properties from the logback project, going on "Order and Export" and setting a marker in every checkbox --> Apply and close.
Now my java application is working and don't throw any more the IllegalAccessError.
I also found out at the old logback version that I can add the line <addDefaultStatusListener>false</addDefaultStatusListener>
to the appender definition to fix the IllegalAccessError. More information here.