Simple answer, yes, and no.
Various MediaCentre versions have the software built in, and you can buy (or download free) TimeShift or recordinging software, but your PC must have the hardware in to do it.
I'm guessing your PC has a HDMI output, and that's exactly what it is, an output, you can't use it for an input signal, the same way that you can't use the input on your TV to broadcast.
You can buy all kinds of TV PCI/PCMCIA cards, Dongles and other USB devices to connect Aerials, cctv
, Camcorders and the like to your PC/Laptop, they can be quite cheap and most will come with the basic software to record with them.