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The interference channel with a relay (ICR) is the fundamental building block of cooperation in wireless networks where there are multiple communicating pairs interfering with each other. This paper considers ICRs in which the links are subject to i.i.d. fading, and each node has channel state information (CSI) only on its incoming links (receive CSI). Two channel models are considered: phase fading and Rayleigh fading. Strong interference conditions are derived for the case where the links from the sources to the relay are good in the sense that the achievable region for decoding both messages at the relay contains the maximal achievable region at the destinations. This leads to the characterization of the capacity region for such scenarios. This is the first time the capacity region of the ICR is characterized for a nondegraded, noncognitive scenario, with a causal relay when all links are active.