A319 Capitan describes a #2 FMGC failure that does not cause the #2 Autopilot to disengage and results in descent below programed altitude on the RNAV arrival.

Narrative

During the descent we received a 'CAB PR ELEV FAULT' ECAM. I called the ECAM and told the First Officer that he had the airplane and radios and I would run the ECAM. After completing the ECAM we then lost the First Officer's ND display (map). While this was going on we were descending using the 'Managed Altitude Setting SOP'. There were a few more warnings and inoperative systems and the First Officer's MCDU locked up. We started to suspect a failed FMCG but there was nothing that made this clear (after landing we realized we should have looked for the 1FD1 on the PFD). The airplane was on autopilot #2 and never kicked off. The altitude alert was set for 7;000 FT which was the lowest altitude on the arrival. Approach asked for our altitude and when I looked up from working the failing systems I saw we were at 7;000 FT. I then looked at my map and saw that the altitude constraint showed we should be at 8;000. I told them we were at 7;000 and I told them we were 1;000 FT too low. Approach told us to maintain 7;000. I double checked and saw that the #2 autopilot was still on and that all the correct annunciations were displayed. It was about this time the airplane needed to make a lateral course change. I noticed that the airplane was not making the required turn. I told the First Officer to turn off the autopilot and hand fly.Here are the highlights. While working the ECAM and trying to figure out what was failing we did not monitor the altitude constraints and trusted the auto-flight systems. Because of the failure of the FMCG #2 the auto-flight system did not adhere to the displayed constraints. I did not know that the autopilot would stay connected and the F/D would display guidance with unreliable information. I am not sure what the autopilot was doing but it was still our fault for not monitoring the flight path.