I only ever had luck by installing the Intel driver first, a lot of the time the driver is modded by the notebook manufacturer to accommodate the switchable video feature, then installing the secondary video driver also from the laptop manufacturer. A lot of the time we see these issues after a update to the secondary driver either through Win update or initiated by the user. Try installing the HP Win 7 drivers in compatibility mode the Intel first then the ATI but there have been a lot of issue with switchable graphics in Win 8.1 preview(keep in mind the preview is a beta not a finished product, even the 8.1 RTM released on technet this week is not all the final bits and pieces I'm hearing).
