Not really a problem; you should be able to do this easily AND it's legal, even if you have to use the "double install" trick (it's legal because even if you don't use it, you DO (did) have a qualifying previous operating system). Windows SHOULD recognize the PC as the same PC on which that same product key was previously installed, and you SHOULD not have any activation problems. As long as it's the same product key on the same hardware, you are allowed an infinite number of reinstallations.
Ok, to start:
1. Save everything (ideally) or, if that is not possible, save everything you think that you might need.
2. After Windows 7 is installed, you are going to need to reinstall all of your applications programs from their original media, and you are going to need Windows 7 drivers for all of your hardware. Now is a good time to collect those.
3. Run the Office settings savings tool for the version of office that you have to save your office settings (on office 2003, it's the "Office 2003 Save My settings Wizard" and it produces an OPS file.
4. Run the Windows easy transfer tool and, likewise, save your settings. I would save settings only, and not any files. Or, if you think that your settings are badly screwed up, skip this step.
5. Boot from the Windows 7 DVD and do a "clean install". There are "advanced options" that will let you destroy existing partitions, if any, which I would recommend if you are sure that you have saved everything necessary back at the beginning.
6. If you have a product key that won't allow a clean install (the message will be something like "this product key does not allow a clean install") ... well, you can do one anyway. Basically, in this case, you do an install without entering ANY product key and you get a "30-day trial version". That's fine. Make this, still, a "clean install". Don't worry about installing ANY drivers, because in the next step we will "blow away" this install anyway. IMPORTANT: Choose the same "Edition" (Home Premium, Business, Ultimate .... whatever you have) that your product key is for, even though you won't even be entering it.
6a. If you had to use the step 5 process of the previous paragraph, after the install is done and working, do ANOTHER install, this time an "upgrade" install (installing Windows 7 over itself). This time you will enter your product key normally when asked.
[for more information on this somewhat convoluted process, see:
Note that there is some question about whether this is legal in some situations. But in your case, you DID have a qualifying installation of Windows Vista, so it definitely IS legal, based on your description of your situation.]
Ok, now you will have a new, clean installation of Windows 7.
At this point, before you do anything else, if you are sure that you saved everything that you needed, get rid of the folder "Windows.old" IF THERE IS ONE. This will be (if it exists) a saved copy of the old "Windows 7 over Vista" system. Make it gone. If you have it, and if you have trouble erasing it, see: http://support.microsoft.com/kb/933212
Note, again, when you installed Windows 7 by booting from the Windows 7 media, you should have done a "clean" or "full" install, NOT an "upgrade".
Now what's left is installing all of the necessary drivers, all of the "Windows Updates" and service packs, then reinstalling all of your applications and restoring their data (which you saved before starting). All of this can be very time consuming (hours to days) but if you want a truly clean install, that's what you have to do.