I just reinstalled my computer with windows 7 64bit and I have HP pavilion dv7 6050ec with two graphic cards : mobility radeon HD 6770M and a generic Intel HD Graphics Family. Since I reinstalled the computer, I no longer have to option to chose what graphic card I want to use. Before this reinstallation I could just right click on the desktop and there was a option that said Switch Graphical units, but now there is nothing like that. And I have the latest drivers for both graphic cards and latest Catalyst Control Center and Direct X installed. And in device manager all drivers are installed correctly. So I have no idea what to do.
When you did the reinstallation, did you use an installation disc provided by HP, or was it a regular Windows 7 disc. If you didn't use an HP disc, you probably don't have the right drivers installed for your 6770m. For laptops you generally do not get the drivers from AMD's website, as the manufacturers use custom drivers for their graphics hardware. Go to HP's website, and get the driver for your specific laptop.
Another option is to check your power settings. Another way to enable your discrete GPU would be to set a power profile that uses the 6770m as the default display adapter and not the HD 3000. After you do that, simply switch to that power profile before you enter a game, and use one of the default power profiles when you don't need the discrete graphics.