As far as I'm aware of, the PVR accessory for the PS3 (PlayTV) is only available in Europe. Even with this add-on, the PVR accessory does not appear to have any hook-up for connecting a satellite or cable receiver to. There are a few workarounds to turning a PS3 into a PVR (e.g. this example on PVR Wire), but there is a fair amount of work in setting them up and you can't use your PS3 to play games during the recording.
For recording shows to transfer to your PC, there are there two options: A dedicated digital video recorder (e.g. DVD recorder) would let you record the shows independently of the PC, i.e. just pop the recorded DVD in your PC later if you want to copy the show to the PC. The other alternative is to get a capture card for your PC with PVR software. The drawback here is that you'll need your PC on and connected to your Direct TV box for the recordings to take place, but the advantage is that it is a cheaper option to a dedicated recorder.