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I plugged it in and tried to power it up, and it would not until I hooked it back up to the PC again.

The Rio Receiver will not power on from the remote the first time it's plugged in. The circuit that listens for the remote is not itself turned on until the first time you use the power switch on the device itself. It's nothing to do with whether your PC is turned on.

The Reciever is, in theory, capable of turning your PC on when you turn it on: it sends Wake-On-Lan (WOL) packets. However, not all PCs support WOL (usually it's only those with Ethernet on the motherboard), and even those which do usually have it disabled by default (in the BIOS), and it doesn't always work at the best of times.

Peter