It looks like this HP Pavilion DV6 Notebook PC contains a feature called “switchable graphics” but I am not able to confirm that within the Hewlett-Packard documentation.
It is important to confirm first which graphics controller is being used, the Intel® HD Graphics of your Intel® Core™ i7-2630QM Processor or the AMD Radeon HD 6700M Series.
Some computer models give you the ability to switch before turning the system on between one controller and the other. Some other computer models include proprietary software that allows you using both graphics controllers at the same time.
In any case, it seems like you already performed good troubleshooting and this could be a compatibility issue with Windows 10.
Did you confirm with Hewlett-Packard that this computer is fully compatible with Windows 10 before upgrading?
I would suggest getting in contact with Hewlett-Packard in case they are aware about this behavior when updating these computers to Windows 10