I believe you'll have to do the following:
1)
Enable Windows ICS -- Start --> Control Panel --> Network Connections, right click on Dial-up Connection and select "Properties". Then go to the Advanced Tab and check the box that says "Allow other network users to connect through this computer's internet connection", select your ethernet connection from the drop down box, Do NOT check the second box because some computer might poll for the network time or whatever and automatically dial every 5 minutes, or might dialup when you don't expect it.
2) In Ubuntu, there should be a control panel or system configuration menu (I think it's something like System --> Administration --> Networking). Go into it and assign your Ubuntu box a static IP of 192.168.0.40 and a gateway of 192.168.0.1 (it's possible that DHCP will work and automatically assign you an address, but I'm skeptical of the windows DHCP server).
3) Whenever you want to go onto the internet, you'll have to go to your Windows Machine and then dialup. Then go back to your Ubuntu machine and you should have access to the network.
Oh yeah, just to check, you are using a "Crossover Cable" instead of a standard network cable, right? Crossover cables are required to direct connect two computers (switches and hubs will usually do the crossing for you).