Laptop with Video In?

Yes it exists, it's called a video capture card. It's rare to get in a laptop but you can get a USB dongle (search for "video capture USB dongle") to do it.

However it won't necessarily run independently of the laptop processor(s) it will pipe a digital signal in and allow you to then use it on the laptop for display, recording etc.

One thing I'd recommend is to consider a TV tuner, which can often do both what you need as well as receive TV signals (and you can use your computer as a DVR). For those look for a laptop with a "TV tuner card" or look for a "TV tuner USB dongle". Just make sure it accepts the input in the format you want (e.g. S-Video etc).

Thanks a lot for the help!