OK, let's back up and make sure I have this right, then discuss the options.
You have a wireless router downstairs (for internet access) and all these machines are connected to it over wireless. You’d like to have those same machines connected over the LAN via the Gigabit switch for performance reasons, while maintaining access to the wireless router downstairs.
There are two different solutions. The first involves connecting each machine to the Gigabit switch and creating a second network. So let’s say the wireless router’s network is 192.168.1.x. The wired network would need its own network w/ different IP scheme, say 192.168.2.x. But because you don’t have a DHCP server on the wired network, you’d have to manually configure each machine. So, for example, one machine might be 192.168.2.100 (w/ subnet mask 255.255.255.0) and the other 192.168.2.200 (w/ subnet mask 255.255.255.0). Now those machines can communicate w/ each other by referencing each other’s IP address.
But there’s a downside. Windows only supports windows-based name resolution on one (1) network connection (which by default would most likely be the existing wireless connection). So these machines wouldn’t show up in the network discovery processes (e.g., My Network Places). And you couldn’t reference them by name (obviously), only IP address. Not the end of the world, but a bit annoying. To get around the problem, you could update the hosts file on each machine and create a named reference for each of the other machines (the hosts file is essentially a static naming service that’s always checked first) and use those names in your references. But it’s just a convenience, not a necessity.
The other option is to get rid of the individual wireless connections for each machine, and instead use a wireless ethernet bridge to connect the switch to the wireless network. This is a MUCH easier and simpler configuration since you’re only managing a single wired connection on each machine. The bridge manages the wireless connection on behalf of all the wired machines. And now you have access to the router’s DHCP server for the wired connections (so no manual configuration of TCP/IP), and Windows name resolutions works.
[various machines]<-- wires -->[switch]<-- wire -->[wireless ethernet bridge]<-- wireless -->[wireless router]
Essentially you’re relieving the individual machines from managing their own wireless connections. The machines only have a wired connection to the switch, but still have access to everything; each other, other wireless devices (e.g., laptops), and the internet.
Of course, this requires purchasing a wireless ethernet bridge (not too expensive if you know what to look for and where to shop, $20-40 for low end, more if you want extra features). Or you could configure one of your machines into a wireless ethernet bridge. Ideally that machine would be available 24/7 (or at least whenever the other machines needed access, perhaps the server, the one running the database). That machine would have both a wired and wireless adapter. Using the Network Connections applet, you then bridge those connections. Now anytime the other wired machines need to access to the wireless router for DHCP requests, internet access, etc., they’re simply routed over that machine.
Again, using one of your machines to form the bridge is only a good idea if it's available when you need it. If not, then a dedicated device is the better option, both in terms of availability and lower power consumption. But in a pinch, it will at least work, and keep you going until you do purchase a dedicated bridge.
I know that’s a lot to absorb, but networking can get a wee bit complex at times.