Hmm...ok. Well your first copy of windows 8.1 which came with the machine is whats called an oem copy and is non transferable to another machine. Changing the motherboard is considered by Microsoft as 'another machine' which is why you got the activation prompt.
Now with the second copy you bought, a full version I gather, you simply need to boot from the install DVD by changing the boot order in the bios so it will boot from DVD (watch for the prompt on start up 'press any key to boot from DVD' or something like that otherwise Windows will simply ignore the disk and boot up normally. You can't use the activation keys for any other installs other than the one they were supplied with. Hope this helps some..