The BO_trace.ini looks like the default which is good (can't confirm for sure since the screenshot is cut off)
The CMS traces you provide indicate that the CMS is failing to install some default objects because they already exist in the system or the ones that it is trying to install is an older version that what is currently in your CMS database. When you apply a patch, the installer will put some XML files (DFO) which define needed updates to InfoObjects in your system database. When the CMS is started again, it looks to the packages directory for these XML and will try to install them into the CMS database. If successful, the files will disappear from the packages directory and the record in the CMS database is created or updated.
However, if the object already exists in the system database and the version is newer than what is in your packages directory, the CMS will report the problem in the CMS logs as you have provided.
What files do you have in your packages folder on this host under <INSTALL_ROOT>\SAP BusinessObjects\SAP BusinessObjects Enterprise XI 4.0\packages? Can you attach the files here?