You can find the config files for the database specific DBCONSOLE in your ORACLE_HOME under a direcory named with the FQDN of the Host, an underscore, and the SID. eg

myhost.mynetwork_mydatabase

You could try stopping the dbconsole with

set ORACLE_SID=mydatabase
emctl stop dbconsole

Then fiddling with the config files and dir names and then restarting the console.

If that doesn't work then you can reinstall the dbconsole into a database with command line tools. I'd lookup the full set of help on EMCTL.

Update: I had to recreate some DBCONSOLE repositories recently.

The following steps worked well.

Manual DBCONSOLE removal and recreation

1. Remove the existing Windows Service
    Remove HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\OracleDBConsole[SID]

2. Remove the existing setup from the filesystem
    Delete %ORACLE_HOME%\DomainName_SID
    Delete %ORACLE_HOME%\oc4j\j2ee\OC4J_DBConsole_DomainName_SID

3. Remove the SYSMAN schema from the database as SYS or SYSTEM
    drop user sysman cascade;
    drop role MGMT_USER;
    drop user MGMT_VIEW cascade;
    drop public synonym MGMT_TARGET_BLACKOUTS;
    drop public synonym SETEMVIEWUSERCONTEXT;

4. Run the Database Configuration Assistant
    Select the database from the list
    Ensure that the DBCONSOLE option and the Enterprise Manager Repository options are ticked

1. You will need to used logical standby which can be a bit trickier than physical. However, you can't have a physical standby with a different architecture than the primary.

2. Yes, you can make the standby primary. It is called role switchover: http://download.oracle.com/docs/cd/B19306_01/server.102/b14239/role_management.htm#i1026400