Low-temperature scanning tunneling spectroscopy is used to study the local density of states (LDOS) of an adsorbate induced two-dimensional electron system in a strong disorder potential. At low energy, completely confined states of s- and p-character are found in the valleys of the potential landscape. With increasing energy the whole area becomes filled with LDOS indicating percolation. The percolation threshold is marked by a significant decrease in the LDOS corrugation. Interestingly, we do not find a dominating wavelength in the Fourier transforms of the LDOS, suggesting that classical percolation is a reasonable concept to describe the transition.