DLink Router Dropping Signal Randomly?

My wife, daughter, mother and I recently moved into a place together. Since moving in together, our internet connection has been less than reliable. We use a motorola modem and a DLink DIR615 router. I have a desktop with a wireless card, and my mother has an all in one with a wireless card, so we both connect wirelessly to the internet. We also use iPhones and a PS3 for internet purposes. The DLink is my router from my family's old place before moving with my mother. The motorola modem is my mother's from her place. Prior to sharing a household, I never had a problem with the router dropping signal. She, however, did have a problem with it. She was using the motorola and a netgear router. So, with that out of the way, here's what happens. The internet works fine and the network shows as available, but then suddenly the internet just goes out in all areas of the house. The network no longer shows as available. It's fixed by unplugging the router for about 10 seconds and then plugging it back in. I've tried talking to DLink about it, thinking it was a problem with the router. They even sent me a replacement router because we couldn't figure out the problem, but even with the new one it's still happening. I can also add that while we were waiting for the replacement, we connected my mother's Netgear and it continued happening. When the new DLink came, I confirmed that the router has the latest firmware as well, just in case. I can add that since sharing a network, we've been getting an IP Address conflict message on both computers. We both have Windows 7. Can anybody shed some light on this? I have some knowledge of this kind of stuff but what's happening is way beyond my scope.