Flight Crew Last 90 Days 250; Flight Crew Type 250
Situational Awareness; Human-Machine Interface
Aircraft Equipment Problem Less Severe; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued New Clearance; Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Overcame Equipment Problem; General Maintenance Action
Aircraft
Strange flight to begin with.  Deadheaded to ferry aircraft.  Aircraft parked on cargo ramp and started and taxied from cargo Spot 7.  Preflight was normal other than no jetway or pushback.  After takeoff and clean-up tried to engage LNAV.  Initially LNAV engaged and then when autopilot was turned on LNAV disconnected.  Then the autopilot disconnected and would not re-engage until much higher in the climb.  At approximately FL180; the CDU flashed a message which said something to the effect of 'aircraft not located at origination position.'  (That is not exact language but it was something similar to that.)  When I checked the position page; it showed the aircraft still on the ground (i.e.; it still showed the coordinates for cargo Spot 7; Line 2 and not our current position.  Troubleshooting this problem caused us to overshoot our turn on the HAROB 4 Departure at DODVE by one to two miles.  We were just getting ready to ask for radar vectors when Departure Control asked if we were having navigation problems.  We replied yes and wanted radar vectors.  No traffic conflict occurred to my knowledge.  Later on approaching FL250 both LNAV and autopilot began operating normally and when we checked the position page it now showed the aircraft airborne with proper coordinates for our location.  We continued the flight but asked for new routing off of the Q-ROUTES since we didn't have a lot of confidence in the LNAV.  Additional issue was TCAS tested as okay on the ground and was operating on the ground during taxi out but once we got in the air it didn't work again until landing where it worked fine again.  Additional issue was on descent we got a 'low idle' in-flight on the engine.  We handled IAW the QRH.   I believe the aircraft never thought it was in-flight and; to my knowledge; we did everything correct (i.e.; IRS alignment was complete).  We handed the aircraft over to Maintenance upon arrival.
After picking up a B737-300 aircraft to ferry; numerous FMS and navigational difficulties are encountered resulting in a track deviation during departure. Some of the problems cleared up but the crew believed that the aircraft thought it was still on the ground.