First remove any settings that cause the laptop to suspend when the lid is closed, or it may not stay up even once you get it to power on while closed.
If the machine's network card and BIOS support it then you can use Wake On LAN. You may need to enable it in both the BIOS and the laptop's OS.
Once you have determined WOL is available and ensured it is turned on, find the network adaptor's MAC address. Under Linux you can find this in the output from
ifconfig - it is the value listed as HWaddr. Once you know this you can use a tool such as etherwake (found in most Linux distros' standard repositories, you should be able to find Windows equivalents easily) to send out a WOL magic packet that the network card will respond to. For instance if I SSH into my router at home I can turn on my main desktop machine with a script that simply runs
etherwake -b -i eth4 00:1D:60:6E:5E:1A (you will need to change eth4 to be the right interface on your setup, and of course replace my machine's MAC address with yours).
You may find that the laptop will not wake from a fully powered off state - my old laptop would only respond to WOL packets while in a suspend-to-ram state (not suspend-to-disk or fully powered off). Also I very much doubt if WoL will work over wireless in any case.
A quick Google finds an article from Jeff Atwood that details some of the settings you may need to tweak if your laptop is running Windows: http://www.codinghorror.com/blog/archives/000790.html.