According to HP, that laptop was shipped with Genuine Windows 7 Home Basic 64, not Windows 7 Ultimate. How is that important? I'll get to that in a second.
a lot of games use the Intel HD Graphics driver
A lot? As in, what percentage? How many games use the onchip Intel HD3000 graphics? What games specifically use the ATI Radeon 7670m? Why is this important? Because if by "a lot" you mean EVERY game you try to play, then your problem is simple. When you replaced the OS that the system came with, by installing a fresh and clean copy of Windows 7 Ultimate, you did not use the video drivers provided by HP. You downloaded the most recent and up to date video drivers from AMD/ATI and installed those instead. You most likely also downloaded the most recent drivers for your Intel HD3000 (although I think the Windows install would have taken care of them). This is a problem, because using the drivers that came straight from AMD/ATI won't allow for the switchable graphics setup in your laptop.
Solution? Remove any trace of the AMD/ATI drivers you currently have installed, download the video drivers from HP for your model laptop, and install them.
Oh. How was the replacement of Windows 7 home basic important? You didn't mention how the laptop worked fine playing games before you installed Ultimate.