Now the function IsGenuineEx() returns only 'TA_FAIL' error. What it does exactly mean in this scenario?
It means they're not activated or they couldn't re-verify with the servers. Use IsActivated() to see which case it is.
My guess is they also changed more than their hard drive. Also, make sure you're using the latest version of TurboActivate (currently 3.4.6).
I found in the API file that error flag 'TA_E_REACTIVATE' has As of TurboActivate 3.3 this is no longer used.
Right, because IsGenuine() and IsGenuineEx() both automatically re-activate behind the scenes (rather than requiring an extra step from you to call Activate() again).
Will function Deactivate() help with this?
No, not at all.