Couple of questions:
1. You say "both are accessible" - what do you mean by that? Do you mean both NICs are on the same LAN segment? So the "internal" NIC is able to talk through your hub to both the PC you are trying to boot and your broadband router? If so, then this can easily be the cause of your problem.
2. What does the PC do when it fails to boot? Do you see the PC acquiring an IP address? Does it fail to get one? Or does it get the IP address, and start saying that it is accessing the TFTP server, but then fail at that point?
The answers to both these questions are critical to whether you will get this working or not. The first because if your broadband router can see the DHCP requests, it could be getting in first and supplying an IP before LMCE does. You CAN add MDs manually, BUT you should never have to if you have set your network up correctly and there isn't another problem (like dead DHCP server) which needs to be fixed anyway. Plus if you do it manually, you are likely to be setting up more complexity than you need, and could mask other problems. Start by removing the manually added MD as this will prevent you from being sure that everything is working fine.
Also, separate your internal and external networks physically, if this is how they are set up. There are also DHCP lease issues with the core if you try to REnew an old lease from your broadband router even if they are no longer on the same network together - but this should only effect non-network boot devices like NAS's and Windows shares for your media. Either way, double confirm that the IP address your MD gets is not only from the core, and on the core's internal subnet, BUT also in the small sub-range that the core sets up by default for this, can't remember the exact range but its something like 192.168.80.20-40 (not the entire 80 subnet)