Internet connection fails very frequently!

Question

I use a Wired Router D-link Dir 100. There are 4 of us sharing a single cable internet connection. The router is connected to the cable modem and all other 4 computers are connected to the router. The past week the internet connection used to fail a couple of times a day. To establish a connection again I restarted the modem, and then most of the time the internet connection would come back. I tried calling my ISP and they told me that the modem is fine. I checked the router and noted that when the internet connection, and I try to renew and release the DHCP no IP addresses appear and the router says that "DHCP client is not connected". After I restart the modem the problem is fixed. Last time I tried restarting the router and that fixed the problem. I set my router on Dynamic DHCP. I tried setting up a static DHCP and that did not work for me ( maybe I did not know how to set it up properly),I am looking forward to your reply,Thank you for taking the time to read this letter my email [e-mail]