With two PCs on a switch that's directly connected to a modem only gets an IP address. You need...or need to mention....a router. As well, VPNs can be tricky as far as DNS resolution. Sometimes you need to manually add that DNS in your network settings.
I have 2 computers on a Linksys EZXS55W switch and I can connect to the internet with either one. However, if I try to log on to a VPN the VPN will not accept the out put of the switch and I have to connect the cable modem directly to the computer that I'm using to log on to the VPN in order to connect to the VPN. Is the switch doing something to the signal that the VPN doesn't like? Any help with this will be appreciated. I'm trying to avoid having to remove the modem cable from the switch and plugging it directly in the computer that I'm using to log on to the VPN.