What OS did you laptop come with?
If it's W8 or later, the 'key' I believe is stored in the BIOS/Mobo (not sure of the inner workings). AFAIK, changing the HDD does not classify as "significantly changing the hardware" and you should be ok. You would just need to reinstall windows from USB or disc and it should activate when you connect to the internet (W10 works the same way).
Unfortunately, if it's windows 7 or prior, you do need the key. As Milheim says, it should be on a product sticker underneath your laptop (sometimes beneath the battery).
If windows has been reinstalled before, you could use a key 'grabber', as there are numerous programs out there that will do this. If the OS is as it came from the factory however, then this won't be possible, as it's grab a generic key that won't work for re-activation.
If it