"False-negative ELISA results: Patients who have negative results on ELISA but positive results on PCR are usually considered to have false-negative results. False-negatives results are probably most common very early after infection (it takes 6 to 8 weeks for third-generation-ELISAs to yield positive results vs. 2 to 3 weeks for PCR) or in patients who have an impaired immune system"
http://www.ahrq.gov/clinic/3rduspstf/hepcscr/hepcrevapp.htm
One of the tests was wrong. Probably the first one.