Simple answer is "no" because you would be running Internet Connection Sharing in two PCs in the chain. The ICS "host" always has the IP address 192.168.0.1 and you cannot have two PCs in the same network with an identical IP address.
In your friend's case, the router and his internet connection must have had a LAN IP address other than 192.168.0.1 so that this address was available for the network adapter that you connected to in his PC.
...though why you connected to his PC and used ICS instead of connecting directly to the router seems strange, unless it was only a single port router.
What you could try is to plug a Wireless Access Point into your desktop PC's network adapter and then run the two laptops "wirelessly". While this should work OK, in practice there does *seem* to be a problem with multiple ICS "client" PCs if a client is running Windows 98. There doesn't appear to be the same problem with Windows ME or XP.