Ron presents an interesting theory.
Using AMD's Magic Packet, it is theoretically possible (under specific controlled conditions) to send the WOL packet to a specific MAC address, although it really should be broadcast to the entire segment - the MAC address that you're trying to power on is actually coded into the data segment of the packet.
However, even if the packet is sent to a specific MAC and the ARP cache on the switch has expired, the switch should broadcast the packet on all "unused" ports since it doesn't know which port that NIC is attached to.
In my experience (3com NICs) the link led should stay on and the activity led may or may not flash randomly as broadcast packets are received.
Antoniov,
That Solarwinds writeup is incorrect - it has a line reading "You must also identify the IP Address and MAC Address of the remote device".
The IP address of the remote device is NEVER required.
IP addresses are logical, when the host device is powered off that IP address ceases to exist.
If the sending workstation and the remote device are on the same physical network segment only the MAC address of the remote device is needed. The WOL packet is normally a broadcast.
If the sending workstation is on a different network segment to the remote device, the WOL packet needs to be routed to that segment, so the broadcast IP address of the segment should be entered, along with the MAC address of the remote device - the IP address is used only for routing purposes. If the IP address of the remote device was used, and the MAC address corresponding to that IP address was no longer in the ARP cache of the router, the router would send an ARP request to find the MAC address that matches, receive no response (because the device is off) and simply discard the packet.
Incidentally WOL works in a DHCP environment, where the host device doesn't know it's ip address until after it's powered on.