Well, first thing I would try would be to give the problem computer a static IP address (this is assuming that you have already made sure it is not the cables).
So, go to "Start->Control Panel->Networking" right-click on the local lan network that exists for your system and go to properties. Click on the "TCP/IP Protocol" and a new window will pop-up. I forget where exactly (it might be one of the tabs), but there will be a screen that has "Use DHCP" with a selection box next to it or "Specify IP Address" (or something like that). Click on the "Specify IP Address" and it should then highlight a group of 4 input boxes where you can type in the IP address you wish to use. You need to know what IP subnet the rest of your network is (for example 192.168.1.xxx), and then specify an IP address, I suggest something like 192.168.1.40 since you don't want the Dlink router trying to issue a DHCP requested IP address to another system with that address (don't worry this is only temporary we just want to find out the problem at this point). You will also need to setup a default route (usually 192.168.1.1, or whatever the address of you router is). Then click on the "OK" and "Close" buttons and it should set that as the IP address of the problem system.
Now check to see if you can connect out to the network. If you can't, does the router have a "link light" on it which says that there is a physical link from the problem system? If the light is out, then you either have cable problems, the network port on the router is bad, the network card in the computer is bad, or the network card in the computer is not setup (maybe you have two network cards and the one you configured is for the other one). Test the port on the router by connecting the other wired computer to it and see if it has any problems (using the cable that the good computer is using, since we know it is a good cable). If the port works, try swaping the known good cable with the unknown cable (i.e. the one connected to the computer that doesn't work) and see if you get a link. Now that we have tested both cables and the port, we know it is either the network card in the computer or the computer does not have the card properly installed... Go to the "system" screen (start->control panel->system) and then the "hardware" tab and look for red X's or yellow !'s... If you have any of them, then things are not configured or working properly, most likely need new drivers for the hardware. If that doesn't fix the problem, you might have IRQ or interrupt conflicts, so try changing the PCI slot that the network card is connected to (or if it is built into the motherboard, open up your user's manual and find out what PCI slot shares its IRQ or interrupt with the network port and move any PCI card that is connected to that shared PCI slot to a new location). If that doesn't fix the problem, then you have a bad network card...
Again, this goes from the assumption that everything is new (i.e. new network cards, new router, new cables). If you used this network card in this computer before in the past, then you know the network card is not at fault. Use this kind of information to track down what the problem is....
