How exactly are you defining "a non-Internet wifi network" ??
You may want to open a command prompt and run
ipconfig /all
one time when it's connected and one time when it's not and compare the results
And check your security suite whatever that might be, if it has a firewall component then you'll need to make sure that the problem network is trusted.
Can we assume that when you connect to an actual normal wifi network that you don't have this problem?