It really would have been helpful if you had said, I have a server at x.x.x.x using x adapter with a default gateway of x.x.x.x, and it connects to the NAS but not the Internet. And I have a wireless adapter with y.y.y.y, with a gateway of y.y.y.y and it connects to the Internet and the corporate network. Ans how they ALL are physically connected. It is really hard to get a hand on what you really have. So I am kind of guessing, so I will give you three things to look at.
First, you could just take out the default gateway on that connection which connects to the NAS but not the Internet. Even if they are on the same x.x.x.x network, the LAN traffic should attempt to use the faster Interface, and other traffic will have no choice but to use the Wireless interface to get to the network.
You can combine this by changing the metric of the LAN to 1, and Wireless to 2 to guarantee that it gives priority to the LAN (even if it should by default).
Lastly you can look in your network connections Control Panel applet, and go to Advanced>Advanced Settings, and play with the binding order. I cannot be more specific since I have no idea what your configuration really is.