How to re-activate Windows 8.1 after mother board change?

I have bought a Dell Laptop 2 years ago which came with Windows 8.1 Home edition. The Hard disk which came with the laptop is still there and it contains the Windows 8.1 installation partition. But, due to a problem of motherboard, I had to replace it. The laptop came with i5 4th Generation processor, now I installed i3 4th generation as i5 was not available.

When I start the system I see Windows is not activated. I don't remember the product key that came with the Laptop. It doesn't seem to be there printed on the Laptop.

I tried activation via phone, but the installation id shown in Windows seem to be that of the new motherboard. The old mother board is not there now. So it didn't get activated.

The DELL Laptop is Inspiron 15 3000 (bought from US) which came with i5 processor, @ 1.7GHz Windows 8.1 Home, 8 GB RAM in year 2014.