I suggest you take the router out of the equation.
Turn off both your computer and mbw. Disconnect your pc from your network. Connect the mbw directly to your pc.
Turn on the pc, and once it is up and running turn on the mbw. Give it a couple of minutes.
I'm assuming Windows PC, so open a command prompt on the pc and type 'hostname', then ping the hostname- it will probably be in the ip range 169.254.xxx.xxx Now try 'ping mybookworld', that should return the ip address of the mbw.
Either way, you should at this point be able to open a web browser, and just type "mybookworld" and be connected to the drive. Alt: use the ip address that the ping returned.
If this works, then your problem is with your router config.
I have my mbw attached to a router too. I left DHCP turned on in the mbw, and I have my router assign it a fixed ip address in my home network range. ie 192.168.0.200 . That is normal procedure for a shared network resource such as a network shared hard disk- that way all computers on my home network always know what ip address the mbw should be, and I don't have to worry about resolving its actual name.
Hope this helps.