When Windows is installed it recognizes information from the chipset and becomes part of the startup process. If you take a hdd that has had Windows installed on one computer and then install it in another it will see different information from the different chipset. The operating system becomes confused and may not start, if it does there's still a good chance that it will eventually not start. Your computer may be the same model, but there could be a difference in the chipset.
You could install it in an external enclosure to connect it to the new computer, then download a program like Ubuntu to access you files and transfer them to the new computer's hdd.
How to use Ubuntu to recover data from a hard drive.
Please download Ubuntu
, you will need to burn this to a CD in order to make a bootable disc. To do this please download ImgBurn
When you open ImgBurn you will see a page like the one below.
Click on Write image file to disc outlined in red.
The next page to open will be like the one below.
Click on the icon of the folder and magnifing glass outlined in red to the right of Source to locate the Ubuntu ISO file. Place a CD in the optic drive and click Burn.
In order to boot from this disc you may need to enter the BIOS and make your CD/DVD-ROM the first device in the boot order.