I have a modem that gives me internet and lately I connected to it a Dlink router to have wifi. I did configured the Dlink and everything was working well for some days. Suddenly the modem was not giving me any IP through direct cable connection. I just remove the cable from the modem to the router and then everything was working again.
What model D-Link router do you have? What FW is currently loaded on it?
What Mfr and model is the ISP modem?
I recommend that you have your ISP check the cabling going to the ISP modem, check signal levels going to the ISP modem. For DSL or Fiber service lines, ensure that the ISP is using good working phone or cable lines to the DSL modem and that the phone lines are filtered correctly. For cable Internet, RG-6 coaxial cable is needed, not RG-59. Check for t.v. line splitters and remove them as they can introduce noise on the line and lower the signal going to the ISP modem. I recommend having the ISP service physically check the lines going from the out side to the ISP modem. Connecting to the ISP modem could result in a false positive as the signal to the modem could be just enough to that point then adding on a router, could see problems. The router operation is dependent upon getting good data flow from the ISP modem and the modem is dependent upon getting good signal from the ISP Service.
This sounds like you might have an address conflict, caused by 2 routers. You should be running your wired connections through your router as well as the wireless.