One example is Mendellian genetics. Because any allele has only half a chance of being passed on to the next generation, the spread of even favorable mutations is pretty much impossible. In addition, a gene is so complicated that the creation of new ones, coding for new faculties, new phenotypes, is also practically impossible.
As for your other point, that new functions cannot arise by chance: proteins only contain a handful of structures. It is by mixing and matching the structures that are there that new functions arise. Proteins that act as environmental sensors of oxygen, of "xenobiotics" (environmental compounds ingested or absorbed by the organism), or light sensors have a common structure and are present in organisms as varied as plants, insects, bacteria, and animals. Organisms are constantly shuffling genes and parts of genes; it is how we believe that novel functions arise. Now, as to how the proteins originally arranged themselves into functional structures, or how thousands of proteins work together to sustain life... these are questions which make many scientists wonder about intelligent design. If there was a creation event, it had to happen billions of years ago, and involved simple organisms such as viruses (which are not truly alive) or bacteria.