The pilot of the Piper PA31 had submitted details for an IFR flight from Lord Howe Island to Sydney via MAGOO and CHEZA at 9,000 ft, estimating CHEZA (60 NM from Sydney on the 084 radial), at 1835. At 1825 the pilot called Brisbane Centre for a clearance and was instructed to squawk transponder code 2350. The aircraft was identified at 50 NM from Sydney, on the 059 radial. This placed the aircraft some 22 NM right of track, within controlled airspace, and in potential conflict with an outbound Boeing 747. The pilot of the PA31 later reported that he had been initially tracking on a bearing from the Lord Howe Island NDB. However, at the time of the incident he was unable to receive any Sydney radio navigation aids, and was navigating on time intervals and dead reckoning. The PA31 was squawking transponder code 2000 prior to calling Brisbane Centre. The crew of the B747 did not receive any Traffic Alert and Collision Avoidance System (TCAS) warning. Brisbane radar did not record any transponder returns from the PA31 prior to the aircraft squawking code 2350.