There is a strong need for low-cost biosensors to enable rapid, on-site analysis of biological, biomedical, or chemical substances. We propose a platform for label-free optical biosensors based on applying the analyte onto a surface-functionalized photonic crystal slab and performing a transmission measurement with two crossed polarization filters. This dark-field approach allows for efficient background suppression as only the photonic crystal guided-mode resonances interacting with the functionalized surface experience significant polarization rotation. We present a compact biosensor demonstrator using a low-cost light emitting diode and a simple photodiode capable of detecting the binding kinetics of a 2.5 nM solution of the protein streptavidin on a biotin-functionalized photonic crystal surface.