Did you set the
width to the panel native resolution?
Made sure your laptop is in high power mode when trying to run the game? HotS is very resource intensive and energy saving might cause compatibility problems. Even when plugged in, the system might not be running in a performance orientated profile.
As a temporary test I would suggest disabling your Intel integrated graphics to see if that helps incase it is trying to run from the wrong GPU. Since you are using a laptop if this does work this is not a good permanent solution as the integrated graphics are needed for good battery life.
When your hard drive was repaired I assume they reinstalled the OS? It is possible a vendor specific piece of software was not installed which is required for correct functioning of the system. Check the vendors website for software downloads and anything related to power management, overclocking, performance enhancing, etc might need to be installed for the system to function correctly. Laptops are especially tricky with regard to this as they often use OEM specific boards and such hardware which will not operate correctly with the default generic drivers intended for consumer branded products.