I'm no expert in networking, but I'll endeavour to solve your problem.
First, some clarifications on your hardware setup.A wireless broadband isp? Do you have some kind of wireless access point to connect or a special modem?
Is the dlink "switch" some kind of all-in-one setup? What model is it?
Do both PCs connect to the "switch"? Cable or wireless?
Next, the network itself.How do the PCs connect to the network? Are they assigned IP addresses? Do you manually set them?
What are the assigned IP addresses? What are the gateway entries? Is the gateway address the address of the "switch"?
What happens exactly when you both try to connect to the same multiplayer games?