Yes, from Windows 7 and onward, you'll find that most (if not all) OEM installs of Windows have the Product Key burned in to the motherboard, which will be automatically read by Windows during installation and activation. However, you'll still need to get as far as installing a fresh copy of Windows 7. One easy way to do this is to contact your manufacturer. Go to their website and contact their support team. They will typically be able to provide a link to an installer that typically includes any custom drivers you'll need, or you can purchase a CD/DVD disc from them.
Microsoft allows you to reinstall Windows 7 using the Download Windows 7 Disc Images page, but you'll need your product key first. You should be able to use NirSoft's Produkey to recover your key, then download the ISO from the Microsoft site, then nuke your hard drive and reinstall from a USB stick or disc. A simple search on your favorite search engine should also yield results for recovering the key using a PowerShell script or something similar.
As a last resort, you might borrow a Windows installer disc from a friend, if anyone has one laying around. The installer is only concerned about your key being valid, which should be the case if it's pre-installed on your laptop. I would recommend not doing this if you can get a disc from the manufacturer or directly from Microsoft, if only because the disc you borrow might not be compatible. If you go through the installation process and you're asked for a product key, you've installed the wrong version.
Finally, instead of doing a full nuke, try pressing F5 or F8 when the computer initially boots up, and in the boot menu, choose the Recovery partition. This is typically an area provided by OEM installs that contains a copy of the Windows installer you can use to reinstall Windows, without needing to nuke the system. You can delete the primary partition during the reinstall process if you'd like. Nuking is rarely necessary from Windows 7 onward.