This engine will crank, start and shut off after five seconds or so of running?

During the brief time that the engine does run after starting all of the dash warning lights stay illuminated. When the "engine" relay is removed from the E/C fuse box, the engine will start and continue to run, but the warning lights for the O2 sensor, battery, low fuel level do not illuminate with key on. With the engine running if the "engine" relay is installed the engine will continue to run but all the dash lights illuminate.
We have replaced the relay twice.
We have tested the alternator.
We have substituted a new electrical ignition switch.
We have checked for stored codes (12) indicating no problems.
The problem was intermittent at first, no it is consistent.
We have wiggled the engine harness.
We have checked all fuses and fuse links.