Two years of microwave background observations with the Cosmic Background Imager ( CBI) have been combined to give a sensitive, high-resolution angular power spectrum over the range 400 < l < 3500. This power spectrum has been referenced to a more accurate overall calibration derived from the Wilkinson Microwave Anisotropy Probe (WMAP). The data cover 90 deg(2), including three pointings targeted for deep observations. The uncertainty on the l > 2000 power previously seen with the CBI is reduced. Under the assumption that any signal in excess of the primary anisotropy is due to a secondary Sunyaev-Zeldovich anisotropy in distant galaxy clusters, we use CBI, Arcminute Cosmology Bolometer Array Receiver, and Berkeley-Illinois-Maryland Association array data to place a constraint on the present-day rms mass fluctuation on 8 h(-1) Mpc scales, sigma(8). We present the results of a cosmological parameter analysis on the l < 2000 primary anisotropy data that show significant improvements in the parameters as compared to WMAP alone, and we explore the role of the small-scale cosmic microwave background data in breaking parameter degeneracies.