Well, it sounds like you can play HD video just fine, but a "meager" video card definitely won't help when it comes to editing the HD video. How fast is your video card? 256MB, for example, is pretty low when it comes to working with HD video, but it can be made to work (that's what I have). Anything lower and you can pretty much forget about cutting HD.
You say "Intel dual core" - what are we talking here? 2.8 GHz? Less?