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?