The basic answer is that you need to replace the main board with a PC motherboard, tuner, frame grabber, and Graphics board. Some of it will require that you make mechanical modifications to brackets, and some rewiring to get access to the IR and LEDs.
I'm not aware of a version of Linux that you can load on it, but there may be one. In general, though, the processors in TiVo's don't come close to the performance of even cheap PC motherboards, so getting that to work is iffy at best.
I can answer specific questions about how to interface to the chassis if you need that, but it's too much to put into one posting.