Looking at a photo of the HR-15 receiver, I can see there are no Firewire/IEEE-1394 ports on the unit. There are what appear to be two USB ports and an eSATA port; neither of these ports will allow you to transfer content from the unit. The USB ports are "type A" ports, i.e., USB host ports (for connecting a USB peripheral device to); they're fundamentally different from the ports on a USB peripheral device, so you can't just get a cable and wire them together. The eSATA port is for wiring up an external disk for storing shows; I'm not sure if that was ever enabled on the HR-15, but that won't allow you to download shows from the unit either.
I'm afraid whatever shows you have in the unit are there, and can't be extracted. Sorry.