A couple of years ago the motherboard on my company provided Dell laptop died. They sent me a newer model Dell laptop and I was simply able to swap the hard drives then update the drivers to the new laptops spec. I like gaming and tried to do the same thing with another yet newer Dell laptop I purchased running a good gaming card but this time the new machine wouldn't boot up using my old hard drive. Both computers are running i5 and i7 CPU's the main difference is the video card. Can anyone give me suggestion as to why swapping the hard drive didn't work this time?

MBR or GPT?

 

 

Perhaps Secure Boot is On. You might need to turn it off and enable the CSM.
 

Windows installations are hardware related. The first 'upgrade' I would think you got lucky as the hardware differences between machines were minimal. This newer laptop may be a step beyond with significantly different hardware beyond just the VGA. You say, "Both computers are running i5 and i7 CPU's" which infers the older one is i5 and the newer one i7 ? As the Dixie Chick famously sang, "There's your trouble."

Since you say the main difference is the video card, you can put the HD back into the old computer and remove the video driver. Shutdown, then try it in the new computer. If that doesn't work, in the old computer you can first go through sysprep to remove all the drivers. http://www.howtogeek.com/239815/why-cant-you-move-a-windows-installation-to-another-computer/. Besides that, many imaging programs will let you create an image (on, say, an external drive), then restore it using the option of "restore to different hardware." Finally you can use Paragon Adaptive Restore, included in various Paragon hard disk management solutions, and choose  to "Adjust OS" for different hardware.