Next time it happens open a command window and run ipconfig/all. If your IP address is all zero's, the client didn't get an ip from the host. The one I would be more interested in is the DNS info. If it's all zeros you won't be able to go on the WWW. If you have an IP but no DNS your LAN side will work but the WAN won't. I am so glad I got rid of ICS and got my router. A trick that has worked for me when ICS doesn't, is to uninstall it, reboot and install it again. Then run the wizard again. I use static IP on my lan, I find it makes for less trouble. You can use a static IP for the client. Just remember you have fill in all the blanks, IP, subnet, gateway, and DNS.
I don't know the same things you don't know.