One Public LAN connection, one private, no internet access

Hello,

I have one PC with two ethernet connections. One connection is a simple private LAN, as it is dedicated to being the console for an IBM server (connected directly to the server, with its own subnet). The other connection is connected to the public LAN like the rest of our computers, static IP, gateway and DNS. For some reason, when both connections are active, there is no internet access for the PC. I have to disable the "private" connection in order to update A/V, Windows, etc... The PC is always available locally for remote desktop, but cannot connect to the outside. I suspect it is trying to use the wrong network connection (and thus gateway) to reach the internet, but I cannot find anywhere to change this "setting."

Thanks,
3DGE14