I've got two networks, one wireless and one wired, both with different internet connections. I want to connect to the wireless network without using its internet connection. How is this possible?
You can change the priority of the network adapters, to make the wired more of a priority than the wireless. (this is the default with Windows 7, i thought) An alternative to manually changing the metric is to change the binding order. Go to Control Panel\Network and Internet\Network Connections, hold ALT on the keyboard, then click advanced->Advanced settings. move the adapters up and down in the priority you want.
Now, if you want to be connected to both, but NEVER use the wireless for internet traffic, you can either block it at the router device, or modify your routing table and remove the default route 0.0.0.0 to the wireless adapter. Then, it will only go to wireless for the known IP ranges listed, and if its not on your lan, it will always go out your other interface.
I wrote a guide to changing metrics, however I mis-read your question! I will keep it below in case you find it interesting.
Basically, if you have two available internet connections, Windows will always choose wired over wireless by default as it will have a lower metric (see below for more information).
If your network has two completely separate IP ranges (e.g. 192.x.x.x for wired, 10.x.x.x for wireless), it should just work no matter what. If however, you have two IPs on the same subnet/ip range, everything will just go through the device with the lower metric - and unless you want to start messing around with custom routes, there is no easy way around this.
This is because by default, a wired connection has a lower metric (priority) than a wireless one. When you have two possible matching routes, Windows uses the lower metric.
Right click on the device you want to use and click
Change the Interface metric to 1.
Hope this helps¬