You can gain access to a computer when it's "Off" I believe if it has wake on LAN, however, don't quote me on that because I am not sure and too lazy to check. Regardless it would require being on the same network.
Router firewalls filter out public addresses and subnet directed packets. Even if he were to spoof his address to access my LAN and somehow woke my computer that still doesn't get him passed any password or software security. Not to mention the P5KRs WOL is turned off by default.