Product keys for retail computers are always on the side or back of the case. If it came off, that sucks but that is something you'll have to figure out. As others have stated; Tom's Hardware does not support piracy and no one here will supply you with a product key. If you cannot find it, and cannot afford a new copy of Windows, I would recommend looking at Linux as a free alternative.
If the sticker came off, you should have it written down or it is in "your paperwork". Last resort, call e-machines and give them your name and invoice number. If the records are legit, then they should help you.