Yes, this is completely possible. Look into Wake On Lan, and Magic Packets (i'm not joking, that's what they are called). Such services like Logmein, TeamViewer, and GoToMyPC, support sending a "wake up" packet to the NIC on your PC. Similar to a PIX boot option. Often times, these are not enabled by default, make sure your NIC has turned this option on. I have seen issues with DHCP, and attempting to do wake on lan. You may have to set a forwarding rule to do a broadcast, or possibly change to a static IP on the device you are attempting to wake up.
There are other ways to do this, but a pre-built software setup often are easier to get going. The only one of the three I've spent anytime with is Logmein.