OEM machines do include a product key attached. You are licensing the software when you buy that machine, you aren't buying the recovery disk. Grab a clean OEM installation disk from a friend, ask for a copy from the shop you bought it from (a non crapware version that they keep in their workshop) or download a copy. The disk is just an installation media, and has nothing to do with your license of windows.
That said, the disk is still handy. You can call up MS support, claim your sticker has been torn up or damaged, and get a replacement key from them - they will ask for either the part number on the inner ring of the disk, or ask you to scan/photograph the disk.
Additionally you are able to activate your copy of windows online up to 3 times per month, after that you will need to contact them over the phone, and when asked by the automated machine, say that you are installing it on the same computer, and that it is only installed only on that computer exclusively.
