Just make sure I am clear on what you want to do - you want to use your denon remote to control your tv, your Receiver, and your Vaio. You may be able to do this. As you mentioned, programming the remote to control your tv is just a matter of finding the right method/ code for teaching the remote. In order to use the remote to control your computer, you will need to make sure that the ir receiver in the computer is compatible with the signal from the remote (freq, etc). JRiver makes it fairly easy to configure Media Center to respond to your remote.
(I am doing this from memory, but it should be close)
Go to Tools->Options->Remote Control
Click Commands - You should now see a list of commands for JRiver
Select a command and click the 'learn button'
Make sure that your remote is set to whatever mode you want to use to control the PC (Receiver, TV, PC, etc) and press the button that you would like to associate with this command
You need to be fairly close to the receiver (an inch or two) and hold the button down until the command is learned. If Media Center doesn't respond after a few seconds, then it is not receiving a command from the remote and you will need to determine why (the remote isn't sending a command, the ir receiver and the remote aren't compatible, etc). If Media Center responds that it has learned the command, continue on teach the commands as necessary.
There are many other ways to do this with programs like eventghost, etc, but if you can't get this remote to work with the receiver in the VAIO, then go with Jim's suggestion above and buy a media center receiver.
Hope this helps,
Alex