If you purchased the laptop with Windows pre-installed then it is probably an OEM copy and the key for that will differ to a retail copy, or volume license copy, or whatever.
You may well have a restore partition on the drive so you could boot into that for a repair. If not, you may have an application on the machine to make your own discs.
Can you give me the make and model number, please?
like you said samsung have said they can't help with a disc.
It's a Samsung NP-E352-JA03UK
Thanks