Having looked at the DM602 and DI-614+ documentation the first thing I think you'll find is that both devices default to the IP address 192.168.0.1. You can't have both devices on the same IP address, in fact you're going to have to change the LAN sub-net of one or other of the devices altogether.
I also note from the DM602 documention that when it is used in modem-only mode page 5-11 of the manual states "Note: If you change the modem from Router Mode to Modem Mode, your computer must configured with a static IP address of 192.168.0.2-192.168.0.253, a Subnet Mask of 255.255.255.0, and a Gateway Address of 192.168.0.1 to be able to connect to the modems built-in configuration pages."
Thus I would suggest changing the DI-624+ to have a static IP address of 192.168.0.2 on it's WAN port, so that the DM602 can talk to it. On the LAN side of the DI-624+ I would change to an entirely different sub-net such as 192.168.1.0 / 255.255.255.0 or 10.0.0.0 / 255.255.255.0, whereby the router has a LAN IP address of, say, 10.0.0.1 (if the second of my examples isued) and it allocates IP addresses to the LAN as the DHCP server in the range 10.0.0.2 -10.0.0.254.
I would also suggest you read something like the thread (http://bbs.adslguide.org.uk/showthreaded.php?Cat=&Board=dslrouter&Number=1013224&page=&view=&sb=&o=) which, although it does not deal with the DI-624+, does describe some probs encountered by someone trying to use the DM602 in modem-only mode with a Netgear wireless router. Judging by the difficulty they had trying to get 2 pieces of Netgear kit to work together, you could have a struggle on your hands!
But at least get the kit on different sub-nets as then you will be able to address each by a unique IP address and access them via the IE GUI.
I also note from the DM602 documention that when it is used in modem-only mode page 5-11 of the manual states "Note: If you change the modem from Router Mode to Modem Mode, your computer must configured with a static IP address of 192.168.0.2-192.168.0.253, a Subnet Mask of 255.255.255.0, and a Gateway Address of 192.168.0.1 to be able to connect to the modems built-in configuration pages."
Thus I would suggest changing the DI-624+ to have a static IP address of 192.168.0.2 on it's WAN port, so that the DM602 can talk to it. On the LAN side of the DI-624+ I would change to an entirely different sub-net such as 192.168.1.0 / 255.255.255.0 or 10.0.0.0 / 255.255.255.0, whereby the router has a LAN IP address of, say, 10.0.0.1 (if the second of my examples isued) and it allocates IP addresses to the LAN as the DHCP server in the range 10.0.0.2 -10.0.0.254.
I would also suggest you read something like the thread (http://bbs.adslguide.org.uk/showthreaded.php?Cat=&Board=dslrouter&Number=1013224&page=&view=&sb=&o=) which, although it does not deal with the DI-624+, does describe some probs encountered by someone trying to use the DM602 in modem-only mode with a Netgear wireless router. Judging by the difficulty they had trying to get 2 pieces of Netgear kit to work together, you could have a struggle on your hands!
But at least get the kit on different sub-nets as then you will be able to address each by a unique IP address and access them via the IE GUI.