Hooking up more than one computer may be done in one of two ways. Either the Internet source goes into a router, and the computers connect through the router (wireless or wired), or the Internet source goes into one computer, and the other computer connects through the first computer. Unless your desktop has a special, separate, internal card for the DSL AND still has another network connection available, or your desktop happens to have a special card that makes it a "wireless access point," or your desktop has more than one network card, your laptop is not going to the desktop through connection sharing.
That would suggest that you probably DO have a router, or that the two computers are, somehow, able to connect directly to the DSL modem (usually by having one use a network cable and the other use a USB cable). Sometimes, routers can get a little "spaced out," leaving the computers that are attached to them thinking that there is no Internet connection. If you DO have a router - that is, a separate box BETWEEN the DSL modem and the computers, it should be rebooted, too. In case you haven't followed all the necessary steps, here they are, IN ORDER (if you are using a power strip, don't just use its switch - follow this order exactly):
- Shutdown the computers.
- Unplug the power cord to the router.
- Unplug the power cord to the modem.
- Verify that all the network wires are connected properly.
- Wait 30 seconds.
- Plug in the power cord for the modem.
- Wait for the status lights to settle down - at least 30 seconds. Remember that the status light for the computer side of things will not be on yet, since the router and computers are not on yet.
- Plug in the power cord for the router.
- Wait for those status lights to settle down. Again, remember that the computers are not on yet, so the lights representing computer activity on the router won't do anything yet. Since you HAVE turned on the router, though, the "computer" lights on the modem may show some activity as the router initialises.
- NOW start up the computers, giving them time to get fully started, especially if you are running firewall and/or anti-virus programs (as you should be).
- Start up a web browser and try to go to a known website.
Again, if you DO have a separate router, and you've only been rebooting the modem (and computers) but not the router, then it could, very well, be the router that is keeping things from working properly, and the above steps should either fix the problem or at least provide more information for further troubleshooting.
Good luck!