Hugo Chávez dominated the Venezuelan electoral landscape since his first presidential victory in 1998 until his death in 2013. Nobody doubts that he always received considerable voter support in the numerous elections held during his mandate. However, the integrity of the electoral system has come into question since the 2004 Presidential Recall Referendum. From then on, different sectors of society have systematically alleged electoral irregularities or biases in favor of the incumbent party. We have carried out a thorough forensic analysis of the national-level Venezuelan electoral processes held during the 1998-2012 period to assess these complaints. The second-digit Benford's law and two statistical models of vote distributions, recently introduced in the literature, are reviewed and used in our case study. In addition, we discuss a new method to detect irregular variations in the electoral roll. The outputs obtained from these election forensic tools are examined taking into account the substantive context of the elections and referenda under study. Thus, we reach two main conclusions. Firstly, all the tools uncover anomalous statistical patterns, which are consistent with election fraud from 2004 onwards. Although our results are not a concluding proof of fraud, they signal the Recall Referendum as a turning point in the integrity of the Venezuelan elections. Secondly, our analysis calls into question the reliability of the electoral register since 2004. In particular, we found irregular variations in the electoral roll that were decisive in winning the 50% majority in the 2004 Referendum and in the 2012 Presidential Elections.