Hi ATK-OK-US, welcome to the HP Forums. I understand you are experiencing Bluescreens when your Radeon GPU is selected while viewing Flash video. I know you would be happy to simply have the option to adjust your brightness levels. Unfortunately using the manufacturer drivers can have unexpected results, which is why HP recommends using drivers provided by HP.
Regardless, I have included 3 different documents on regaining control of brightness. Try each one in order:
Resolving Problems with the Brightness of the Display
Using the ATI Radeon Vari-Bright Feature
See if you have an option to turn adaptive brightness off. You may not with Home Premium: How to enable or turn on and use Adaptive Brightness in Windows 7
Beyond that after a complete restore, Bluescreens could be a sign of hardware issues. Take a look at the section "Symptom: Error message displays on a blue screen" in this document for troubleshooting: Computer Does not Start (Windows 7, Vista, XP)
Let me know how that turns out.