From what you say, your neighbour's record is something like this?
2003: Less than 39 paid or credited.
2004: ??
2005: Claimed but not paid due to less than 39 rule; 52 paid or credited
2006 52 paid or credited.
By my estimation, her claim should have come into payment in January 2007, based on her 2005 record. Dependiang on what she was doing in 2004, it may be due to come into payment in January 2006. The only thing may be that she exhausted her entitlement to JB sometime prior to 2005, in whcih case she would have to work for 13 weeks (she only worked 4, you say) in order to requalify. Nevertheless, check it out with the local office she signed at. They may have overlooked testing her claim in Jan 07.