Is it possible to record TV via HDMI?

You are not going to be able to use your hdmi port because it is output only. And you cannot import HD video into USB without spending a lot of money on some additional hardware. There is no software only solution to your project. But there is a very cheap piece of hardware you can purchase online if you can live without the High Def. and be ok with regular video quality.

The cheapest solution to get the audio and video from another source into your computer is via USB adapter. You can just internet search for "USB 2.0 TV DVD Video Audio Capture".. I bought an "EasyCap 2.0 tv dvd capture" on eBay for six bucks to record from my cable box into my laptop and while not "true High Definition" quality, it is great, especially considering the HD ones go for $100 more.

The HDMI ports on laptops is linked to the graphics card and is strictly video OUTPUT, designed to put your display out to a TV, Projector or other display device.

If you want to record TV, you need some sort of tuner card which simply features a HDMI port.

After doing some digging, this is the only one I could find, and it isn't cheap.

HDMI has been out for some time now, but none of the usual companies I deal with seem to have a HDMI TV card, so I guess they just are not mainstream.

You would need to get an external video capture card that supports HDMI input from the likes of Grass Valley or AJA Video. It probably won't support HDCP, though, as recording is precisely what HDCP is intended to prevent, so you won't be able to capture movies or (possibly) video games, at least not in HD.

Here's one box as an example, from AJA Video: the ioHD. This particular item is Mac-only, but I'm sure there's one that supports Windows.

Edit: this one supports Windows 7.