Sounds like 2 separate problems. A power relay may be hanging up keeping the computer alive. The tach runs off of the PIP signal that runs the ignition. First time I ever seen a computer driven car do this! The computer must still be on because it fires the coils and injectors.
When an injector goes out the rest of the bank goes rich because of the air being pumped via the dead cylinder. The oxygen sensor says lean and the EEC tries to fix it.
