Does this computer still boot? If so, go into System Properties and have a look at the Product ID, the second group has three characters, if they say OEM, then its OEM. This is the way it is for Windows 7, you still haven't mentioned which Windows we are talking about.
As for getting your Product Key this is possible using a program called Magic Jellybean Finder. It will decode the Product Key from the registry. As for not having to enter it, many OEMs (particularly with laptops) code a "default" Product Key into the BIOS so that when Windows installs, it uses that key. If this is the case, you most likely have an OEM version of Windows. Is there a Windows Product Key sticker on the case somewhere? Often when Windows installs using these "default" Product Keys, they don't match what actually shows on the sticker. The "default" key is provided to make it easier for users to install Windows.