A non GPS equipped B767 FMC database contains an error which caused the aircraft to track incorrectly on the IAD BARIN 1; then give EGPWS warnings to Runway 19L and finally not track accurately to Runway 1R.

Narrative

This report covers 2 incidences on approach at Dulles fourteen days apart. The NOTAMs state not to fly the BARIN 1 arrival into IAD due to database problems; but the problem is way more complicated than this. Heading to BARIN on the first event; the airplane; on autopilot; kept doing small right check turns while BARIN kept drifting to the right of the Nav display. Finally ATC queried us as to whether we were going to BARIN; then gave us a 45 degree left turn to correct to BARIN. Now on radar vectors we flew to final for Runway 19L. The extension of the runway was nowhere near the actual final for Runway 19L. Flying visual; at around 300 FT on final we got 'Too low terrain'; then the 'Pull up' commands all the way to touchdown and even on the runway after touchdown. I thought that with the next database update; this would be fixed!! Today; with the new database loaded; the airplane flew pretty close to BARIN; but when we were cleared direct to the FAF for Runway 1R; the airplane started the check turns again; with the fix drifting to the east. Knowing to look for this since my last approach; when asked if we had a visual on the runway; we picked it up about 1 mile to the west and did a rather aggressive maneuver to line up with 1R. The Nav display showed us headed directly toward the runway when we were actually 1 mile east. I believe that it was also showing the Runway a little farther north than it actually was. The first incident; in the weather; would have caused a go around due to the GPWS warnings. There also would not have been any way to define our position with the Nav display. Raw data and vectors would have been the only option. The same for the incident today. While we did not receive any GPWS warnings; in the weather; we would not have been able to find the localizer and glideslope without vectors from ATC. If something is not done about this problem; separation from both other aircraft with correctly operating Nav systems and the ground is going to happen when we are in the weather. My suggestion at this time is to notify all pilots that fly the 767; to get radar vectors before BARIN to final approach. I think it is the only safe thing to do until this problem is tracked down. Being a former USAF test pilot; I suggest getting Honeywell involved on an emergency basis to find out what is causing this before someone gets hurt! It doesn't seem to happen until below 10;000 FT; so I'm not sure if it is internal or external to the aircraft.