Ok. First, I need to make the disclaimer that I only have what you put in the question to work with. This means that if it actually turns out that you did things OTHER than what you said you did... it is not my fault that I did not know this information ahead of time. As much as we would love to assume people have performed certain steps, or that they know crucial bits of information.... not everyone has or does.
That said. Are you aware of the Dell Support site? More importantly, are you aware that you can go to the Dell support site, and you can click on Drivers and Downloads, enter the service tag (on a sticker on the bottom of the laptop) and get right to a Driver download page for that model?
You can also just search by model, and get there... as I did here. Now, you left out the detail as to whether you installed Windows 7 32 bit or 64 bit. Does it really make a difference? Apparently not in this case, as the ATI Mobility driver installation file is the same regardless. Of course, I don't know which you have, and it seems that Dell released that model over time... one with a 6000 series, and one with a 7000 series...
So, this is the AMD ATI Mobility Radeon HD 6470 driver download page for your model.
And here is the Dell ATI Mobility Radeon HD 7450M/7650M driver download page for your model.
Of course, rather than just downloading the one for your laptop from one of those two links, I would actually use the service tag on your laptop to bring you to the specific driver download page (as I mentioned above), and you should choose your exact version of Windows from the pulldown menu on the page before you go to the Video section at the bottom and download the appropriate ATI drivers.
You might ask why Windows didn't just grab the appropriate drivers all on it's own with an update? Well... for two reasons. For one, it isn't Window's responsibility to maintain an up to date database of all hardware drivers. That's why manufacturers like Dell provide support sites like this. For another, your AMD/ATI video chipset isn't active when you are in Windows. The Intel integrated chipset is active. Windows doesn't detect anything but the Intel chipset, because that is all that is being used. ATI doesn't detect that the card is present, because for all intents and purposes... it isn't. It is only used and present when there is a demand (like a game). The Dell driver installation program takes this into account, and puts everything into place.
As you already know.... next time, take the hardware drivers into account before you reinstall. But then again... you really just need to remember the Dell Support page (or whatever manufacturer product page for whatever computer you are dealing with).