What version of the Intel(R) Network Connections software are you using? (You can check the Intel(R) PROSet version on the Link Speed tab for a version number.)
If you configure a gateway on one of the other VLANs, does the connection start working for that VLAN?
I want to try to duplicate a similar setup here. Can you give me more information on the VLANs such as the VLAN subnet information? If you want to keep that information private, you can send me the information in a private message.