Well, since I appear to be receiving little help on this forum :(, I'll tell you what I discovered and maybe you can relay to the BESR development team.
This issue with "no mapping between account names and security id's was done" during the BESR 2010 install is likely caused by a problem in your Installshield routine. Perusing the Installshield developer forums, it seems that this type of issue can occur if not careful with the install routine. Installshield has notes and knowledgebase articles discussing this very issue.
I also found the following which stands out in the BESRinstall.log file. Notice the Installshield error message just before COM registration begins. Unfortunately, the log file does not record the COM+ registration error. BTW, I've followed whatever Installshield says I can do on my side and this doesn't help the problem. See here:
Installshield.
Property(S): INSTALLDIR_OK = 1
Property(S): INSTALLLEVEL = 300
Property(S): ISSCRIPT_VERSION_MISSING = The InstallScript engine is missing from this machine. If available, please run ISScript.msi, or contact your support personnel for further assistance.
Property(S): ISVROOT_PORT_NO = 0
Property(S): IS_COMPLUS_PROGRESSTEXT_COST = Costing COM+ application: [1]
Property(S): IS_COMPLUS_PROGRESSTEXT_INSTALL = Installing COM+ application: [1]
Property(S): IS_COMPLUS_PROGRESSTEXT_UNINSTALL = Uninstalling COM+ application: [1]
Property(S): IS_PROGMSG_XML_COSTING = Costing XML files...
Property(S): IS_PROGMSG_XML_CREATE_FILE = Creating XML file %s...
Property(S): IS_PROGMSG_XML_FILES = Performing XML file changes...
Property(S): IS_PROGMSG_XML_REMOVE_FILE = Removing XML file %s...
Property(S): IS_PROGMSG_XML_ROLLBACK_FILES = Rolling back XML file changes...
Property(S): IS_PROGMSG_XML_UPDATE_FILE = Updating XML file %s...
Property(S): IS_SQLSERVER_AUTHENTICATION = 0
Property(S): IS_SQLSERVER_USERNAME = sa
Property(S): InstallChoice = AR