A star does not start off as a planet; you have a large cloud of gas that is collapsing in on itself due to gravity. The majority of the gas goes towards creating the star (more than 99% in the case of our Solar System). However, gravitational collapses can occur several places in the gas cloud, and some of the gas will contribute towards the collapse of far smaller over-density seedlings. If the mass of the smaller collapsing object is large enough, gravity will pull the object together into a sphere, satisfying one of the three criteria we have to classify an object as a planet (see e.g. [this question][1] for more information about such criteria). 

The very large mass of the gas which is going to become a star allows it to collapse in a way where the pressure becomes great enough that the central parts of the cloud start fusing together hydrogen -- or burning, if you wish. You do need simple gases for this type of ignition to occur, as even higher temperatures are needed for more complex atoms to fuse together. This is because fusion becomes less and less energy effective as the atoms become more complex. 

While I have no direct sources to refer you to, you can be decently sure that the Earth wouldn't become a star if it increased in mass without increasing it's amount of hydrogen substantially. *However*, with the great amount of hydrogen present in the Universe compared to the other elements, a scenario like that would not occur, and Earth's hypothetical accumulation of matter would realistically be of gas which would be used for the effective fusion we find in stars.


  [1]: https://astronomy.stackexchange.com/questions/212/what-physical-features-determine-if-a-planet-is-a-major-minor-or-dwarf-planet?rq=1