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DHCP clients remember their server they received after the first broadcast, and when requesting renewal of a lease direct it straight to that server, not broadcast. So as long as that server stays responsive, they will always get their renewals from it not the real router, and the IP address will remain the same.
On that note - the core also remembers where a device was in its DHCP config file. And will allow a lease to be renewed at the same IP address EVEN IF that IP address is not in the configured subnet scope! This caused me a lot of pain trying to work out why my Windows PC share media was no longer available. Briefly I turned on my router DHCP server and it got an IP address from it, outside the core's DHCP range. I then turned it off again and got my PC to renew again. As it couldn't find the router DHCP server any more it went back to broadcasting and the core responded. But it seems that the PC didn't only broadcast for a new lease, it requested a renewal of the existing IP address. Even though this was outside the core's scope, because it was in the config file it allowed it to keep that address!! No amount of releasing and renewing or rebooting would stop this because even then, the core's DHCP server still remembered this IP and kept giving it out.
Because it is outside the correct range, the core just didn't seem to want to "see" that share and its media any more. I had to manually remove the entry from DHCP3 server's conf file and release/renew - then it got a valid IP in the range and presto the media was back.
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Interesting. I haven't been able to get my Core to give out IP's, and this seems like what might have happened to my setup. I'm going to check the conf file and see if I can't get this thing straightened out! I still don't have LMCE working correctly because of this DHCP problem and lack of time to figure it out, but now I have something to try! Thanks again!