Very important! What version of InDesign? What operating system?
InDesign—as any other Adobe application—does not allow migration from a backup or from another computer. You have to install it from the original installer.
You have to deactivate it from the old computer (you need not to uninstall it) to be able to use the activation on the new computer.
But be aware that older versions are not compatible with older versions.
It's the latest one (cloud version) and the OS is Windows 7 Pro.
On the second computer, download the Adobe Creative Cloud desktop app, and sign in with your Adobe ID (you can install on two computers). Then download the applications you need.
As Willi points out, you don't want to try to copy the files from the first computer. Install them clean from CC desktop in your case.