Can a computer respond to ICMP request if no OS is installed/ is soft-powered off?

"Sure you could send an ICMP request to a NIC by itself, but where are you going to send it? How can the NIC maintain an IP address without any software controlling it? I'm going to have to say no on this one.

As for true Wake-On-LAN, the card only watches for magic packets. In Windows however, if you set the adapter to Allow this device to bring the computer out of standby, which is not exactly the same as BIOS-enabled Wake-On-LAN, a ping will work when the PC is in standby. It seems to bring the computer to a slightly elevated power state to respond, then goes back into sleep mode. For true Wake-On-LAN when the computer is shut off, a ping does not seem to work."

ICMP belongs to Layer 3 of the stack. This is typically a software layer. What this means is that you will need to have some sort of software running, although it need not be a full fledge OS. All you need is a basic TCP/IP stack running, which can be embedded on the NIC card itself as an alternative. However, you need to have some sort of software running. The hardware generally takes care of Layer 2 and Layer 1 of the stack.