[magicconch]

You could configure BIOS/UEFI to power-on when power is restored (or return to last state). Or use wake-on-LAN, which quite a few consumer routers can send through their web interface.

[burnt-resistor]

WoL is LAN specific, unreliable, and sometimes needs extra wires. Last state and a network-managed PDU/UPS us all you need.