Further to my last reply, things do not look that simple 24 hours on. By the way, I have Windows XP, and I am assuming that you do too.
I downloaded catalyst version 9.3 and ran it. It copied the driver OK but would not install it. Instead it said that it cannot find any driver suitable for my hardware or system. Searching on the Internet, this is a common problem and there are lots of ideas about the cause and the solution.
I have found two things that may help.
First, you can download and run a general purpose radeon driver updater from http://download.cnet.com/ATI-Catalyst-Display-Driver-Wi.... I did this. At one point it asked me what I wanted to do, and I had to choose the option to enable users to install (the other option was uninstall). It ran OK, but I am not sure that it actually updated my driver. However, if you have no driver at all, it might give you one.
If that doesn't work, you can try this, which I have done and does work. You can download Catalyst 9.3 as my last post, but don't run it straight away. You must check your .NET framework version. You must have at least version 2. If you have an old computer you may need to download and install that. Restart the computer afterwards (it doesn't tell you to, but people have reported problems if you don't). Then you can run the catalyst 9.3 installer program. For me, it still said it couldn't find a suitable driver, and the reason seems to be that you can't update the driver on a Dell using drivers from AMD/ATI but instead you are supposed to get them from Dell. To get round that, go to http://www.hardwareheaven.com/modtool.php and download the Mobility Mod Tool. Follow their instructions carefully (including installing MSXML 6.0 if necessary). This will modify the driver that the Catalyst 9.3 installer program has copied to your C: drive, so that it can be installed even on a Dell or other laptop where you are supposed to go to the laptop manufacturer. When you get to the end of the instructions, you will have installed your new driver. I did this and it works. However, the driver has been modified and no longer meets the WHQL certification.