Hi Daniel,
From what I can comprehend, You are using the WinGate Internet Client (WGIC) to share the internet connection from the WinGate server. But the WGIC is not working.
1. Can you first check if the Windows XP firewall is enabled on the client machines (and the server for that matter)? You may want to disable it for the sake of testing.
Right Click My Computer --> Manage --> Services and Applications --> Services --> Windows Firewall/Internet Connection Sharing (ICS) --> Double click, set "Startup Type" to disabled, and use the "Stop" button if it is currently running.
2. Sometimes when WinGate is installed it may detect your network interfaces incorrectly, and firewall the wrong side of the computer. Could you check whether your adapters are marked as Internal / External correctly? Gatekeeper --> View Menu --> Network --> (Bottom center). The network card facing your LAN should be marked as "Internal" and the network card / modem facing the internet should be marked as "External", as shown in the image attached.
3. As a test, can the client computers share the internet connection through the proxy settings of Internet Explorer? (Internet Explorer) Tools menu --> Internet Options --> Connections tab (top) --> As shown in image attached.