There are a few things to check here.
Step 1: First of all, can you access the internet with the PC directly connected to the DSL modem? Try to ping a site (start -> run -> "cmd" then type "ping
http://www.google.com"). If you're getting packets back this means that you are correctly resolving names and your primary computer has the correct ip address information including subnet, dns servers and router.
Once that's working and ICS is enabled on that computer, go to step two.
Step 2: Now, the second computer must be able to access the first computer. Open up the command window as before (start -> run -> "cmd") and type "ping 192.168.0.1". This should return some results -- if it doesn't, there is a problem! Are the lights on your network card (behind your computer) lighting up? What kind of set up are you using? If you're not using a switch of any kind then you're going to need a crossover cable.
Connectivity working between those hosts? Let's finish this up:
Step 3: Leave the cmd window open from step 2 and type "ping
http://www.google.com". If the pings are coming back, you're golden. Use the intarweb at will! If this doesn't work, however, something is definitely wrong. Set your IP address manually following this:
IP address: 192.168.0.2 (2 is symbolic here--if you have more than two increment it)
subnet mask: 255.255.255.0
Gateway: 192.168.0.1
Now, set your DNS servers to match the ones your ICS server uses. If your ISP didn't get you any documentation, go back to your ICS server, open a cmd window and type: "ipconfig /all". The DNS servers should be listed there. Enter those on the client computer.
Now, your access should work. If it doesn't, try following the ICS setup wizard for the server computer and then the network setup wizard for the client computer. Tell it you wish to connect through another computer.