No you can't use the same key as they are two totally different versions of Windows 7. You need to get hold of a copy of exactly the same version of Pro that is on your friends laptop. 32 or 64 bit, retail or OEM. Magical Jellybean Keyfinder if you can get it installed can tell you which version of Pro is installed and Control panel/System will tell you whether it is 32 or 64 bit.
The drivers will have to be downloaded separately from the manufacturers site. The drivers can be installed once Windows is up and running unless you have either no working ethernet connection or wireless connection. In that case you will have to download those drivers on a different machine and use a USB stick to transfer them to to the driverless laptop.
You can also download a copy of Service Pack 1 from MS which will save a lot of time when installing the updates.
Make sure your friend has copies of any installation keys he needs for currently installed software such as Office.
You may be able to download a copy of Pro from heidoc.net and use the key on your friends laptop to validate it.
Otherwise google the laptop model for details.