As mentioned in my previous explanation, think of the cable box, your DCT700, at a mini tv station. It broadcasts on just one channel, Ch 3. You get to choose what that Ch 3 station shows by changing channels with the DCT700 remote. What ever channel you choose, the DCT700 always shows it on Ch3, right? (You might be using the 'line' output from the box but, either way, you only have one 'channel' out)
So, if your new player/pvr has it's own tuner(you didn't state the model # so I don't know), you can use a splitter on your cable to allow it to record a different channel while you watch another one through the DCT700. The limiting factor with this arrangement is: you can only record the 'basic' analogue channels that are on the cable. You can only access any additional 'digital' channels that you might have through the DCT700. (magnet's way is probably better but you would have to turn on your dvd/pvr every time you want to just watch a channel from the DCT700) <See how either of these ways is more complicated?>
I hope this clears it up a little. To add to your possible confusion (just because I can), Shaw provides about 10 'free' HD channels with 'basic' cable so you wouldn't be paying any 'extra' for them. Of course, the catch is you need an HD capable Set Top Box, which the DCT700 is not. If you were to buy a Shaw PVR, you would solve a couple of problems at the same time. First, you wouldn't need a splitter on the cable and second, you would get the benefit of being able to actually record 2 programs at the same time while watching a 3rd that you had recorded previously. Additionally, you would have access to the 10 'free' HD channels that are included as part of your regular cable service.
I understand, completely, that you are not big tv watchers and never have been but, if you 'have always wanted a PVR' and have already updated your tv, you owe it to yourself to at least give Shaw's options a try and check out HD. I think you would be very impressed with the difference in picture and the features of the PVRs. If you call Shaw and ask about what they can offer you as someone who is interested in 'trying an HD PVR', you might be surprised at what they say. You may get a lower monthly bill and a free rental for a year, you never know. A 'free PVR rental' means you don't pay anything to check out the latest technology.
Now, that being said, I am NOT a Shaw employee and will in no way benefit from you making a decision, either way. I have my own set of issues with Shaw but, if they are your only choice for cable (which is usually the case), then it can't hurt to give them a call.
Late Edit: magnet responded while I was writing my response so I apologize for anything he said that was repeated in my post. I'm leaving it in for clarity.