Oxygen had yet to appear in much abundance, and wouldn't until the rise of photosynthesis some time later. One of the difficulties in defining when life began is deciding on what actually constitutes life. However, enzymes and other compounds that control chemical reactions do that quite nicely on their own, yet we wouldn't call them alive. Life is the ability to move around in one's environment. However, lichens don't move appreciable amounts during their lifetimes, yet they're clearly alive.
Life is the ability to grow and maintain a particular body shape or form.
Mineral crystals fit those requirements, as they grow in response to a particular distribution of bonds and bond energy. This is still not really satisfactory - certain arrangements of atoms or clay minerals are perfectly capable of the same thing, though they lack the internal energy source that allows living organisms to replicate spontaneously . The other concepts outlined above are part of the package as well, but life really entails reproduction. In Lecture 6 we outlined the likely conditions on Earth around the time of the origin of life. It's worth also thinking about what environments might support these new organisms.