the rest of the network connected via a PCI card in my desktop machine

Could you clarify how you have your network configured? What does the PCI card do - UTP Ethernet or wireless?

I can comment on the more general case regarding your question about what has to "see" what. 802.11a/b/c is Ethernet, meaning that ALL wireless devices are expected to be able to "see", or "hear", all the other wireless devices on the network.

Anytime one or more wireless devices cannot "hear" some or any of the other wireless devices, they can cause packet collisions, which slow throughput, and can also cause other wierd happenings.

ALL wireless devices must be able to see/hear the Access Point reliably. If there are radio "dead" spots (caused by multipath, metal or other dense material, or just bad luck), you can often work around the problem by shifting the AP or node, sometimes just a few inches or feet. Keep in mind that shallow diagonals through material, such as through a wall or floor at a shallow angle, can be the equivilent of several FEET of drywall or wood thickness, enough to significantly impair the signal.