While installing Exchange 2013 it reports there are Exchange 2003 servers in the network when there are not

One or more servers in the existing organization are running Exchange 2000
Server or Exchange Server 2003.

Installation can’t proceed until all
Exchange 2000 or Exchange 2003 servers are removed.

If you previously upgraded from Exchange 2003 to a version before 2013 then you may not have removed Exchange 2003 or 2000 server properly.  If this is the case you can run adsiedit.msc and find the following location.
Load Configuration
services>Microsoft exchange>first organization>administrative groups>  In here find your administrative group.  Then you will see a “servers” container.  Go in there and delete any name references to your old servers that are no longer in your network.