We present the temperature and polarization angular power spectra of the CMB measured by the Atacama Cosmology Telescope (ACT) from 5400 deg$^2$ of the 2013-2016 survey, which covers $>$15000 deg$^2$ at 98 and 150 GHz. For this analysis we adopt a blinding strategy to help avoid confirmation bias and, related to this, show numerous checks for systematic error done before unblinding. Using the likelihood for the cosmological analysis we constrain secondary sources of anisotropy and foreground emission, and derive a CMB-only spectrum that extends to $ell=4000$. At large angular scales, foreground emission at 150 GHz is $sim$1% of TT and EE within our selected regions and consistent with that found by Planck. Using the same likelihood, we obtain the cosmological parameters for $Lambda$CDM for the ACT data alone with a prior on the optical depth of $tau=0.065pm0.015$. $Lambda$CDM is a good fit. The best-fit model has a reduced $chi^2$ of 1.07 (PTE=0.07) with $H_0=67.9pm1.5$ km/s/Mpc. We show that the lensing BB signal is consistent with $Lambda$CDM and limit the celestial EB polarization angle to $psi_P =-0.07^{circ}pm0.09^{circ}$. We directly cross correlate ACT with Planck and observe generally good agreement but with some discrepancies in TE. All data on which this analysis is based will be publicly released.
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