Smallbuilder has written an excellent tutorial on how to power on/boot up your computer behind a Router/Firewall remotely over the Internet using a feature called Wake on LAN/WAN. The guide walks you through the complete setup process right from enabling WakeOnLan in your motherboard’s BIOS and the NIC card properties to configuring your router to forward the special WakeOnLan packets to the appropriate computer behind the router through a firewall. They have also showed how to using a Dynamic DNS service if you don’t have a static IP assigned from your ISP.

Update: Try the same from your mobile phone. Download a free Java J2ME WakeOnLan mobile application for MIDP capable mobile devices.