GPU randomly does not show display

I recently bought a used Graphic Card for my System.It is Sapphire R9 280 Dual-X. The problem is that everyday whenever I start my system, there comes no display on the screen while monitor is hooked with the DVI Port of Graphic Card. Instead, display comes through integrated VGA port of the motherboard. The card otherwise seems to be working as its fans do spin properly but no display from any port.

 

However, when I restart the system, it shows the display through Graphic Card and everything works perfectly and for hours without any issue. I can restart it many time and it works great. However, after shutting down the system for 8 hours or more, again when I start the system, there comes no display from the graphic card unless I restart the system after couple of minutes.

 

I checked it in 2/3 different systems having different specs and different power supplies with same result. Once I get the display after restarting the system, it works perfectly fine in all games, stress testing but no display at first boot annoying me on daily basis.

 

Kindly suggest some solution.