We introduce a simulation-based method to compute the information rates of intersymbol interference (ISI) channels with additive colored Gaussian noise and/or signal-dependent Gaussian noise when the inputs are binary and independent identically distributed. The method extends the idea advanced by Arnold and Loeliger (2001), which focuses on the ISI channels with additive white Gaussian noise (AWGN). With the new method, we can compute the information rates of the Lorentzian channel with media noise that represents a suitable model for practical magnetic recording channels. We illustrate the use of the technique via several examples and show that media noise is preferable to AWGN in terms of the achievable information rates, at low signal-to-noise ratios, in particular. We also present examples of turbo codes for Lorentzian channels with media noise and compare the performance with the achievable information rates. The results demonstrate, not surprisingly, that improved detectors are necessary to achieve the channel capacity for magnetic recording channels when the media noise is dominant.