I went through this a while back with video from a Canon HF100. First and foremost, you need a decent CPU and/or video card. I say "and/or" because if you have the right codec, it would utilize the video card in decoding the content. If you have a mediocre codec, most of the decoding will fall on the CPU. You didn't mention what CPU you have in your 1720, but since its most likely not a quad core, I'm going to say that its not enough (my C2D P9500 XPS 16 doesnt do it well enough either.. my AMD quad is OK). You can tell this is the case because when you're playing back HD video, watch your CPU utilization, it will probably spike to around 100% and stay there, your CPU fan will go crazy and you'll think your laptop is preparing for liftoff.
So the question kind of boils down to, which is the best codec. Unfortunately, I can't really tell you. When I was looking into it, CoreAVC came up a lot. They offer a free trial but it costs like $20 to register. CoreAVC, however, is optimized for use with nVidia graphics chips (at the time, not sure about now). So if your 1720 is using a decent nVidia GPU, then this may work for you. My Dell doesnt have an nVidia GPU, so it didnt do much for me.
I also read a lot about PowerDVD. The newer version (v8 or 9, around there) was able to playback HD video. I actually went this route at the time. My CPU utilization dropped by about 50-70% when watching the same HD videos. And as expected, playback was very smooth.
A couple other things, if you install ZoomBrowser and play the video through there, it should play OK. If it doesnt, then your CPU/GPU may be lacking. ZB works OK for me, still not as good as PowerDVD though.. meaning, its still a little choppy at times. And surprisingly, Windows 7 may solve your problems. Windows 7 finally came with the necessary codecs to playback HD video. When trying to play back HD content using Windows Media Player on Win 7, my CPU utilization stays around 40%, not too bad, and it's not choppy.
Edit: Actually, I'm not sure about ZoomBrowser playing back HD video. I forgot that my HF100 came with some video editing software called Pixela. When you install Pixela, it would install its own codec, which was half-way decent at decoding HD video. I'm not sure the 7D's software bundle comes with a HD codec or not. With my current setup, yes, ZB does playback video, but I'm not sure if its using some Canon supplied codec or if it's just using Windows 7's codec. Yeah, confusing.. thats why I stopped looking into it once I got it working.
I'm sure someone more knowledgeable will correct me, but this is what I found when I ran into issues about 6-7 months ago trying to play back HF100 footage. Today, Windows 7 and WMP work fine on the same computer.