What happens when the alarm on a 2000 S Type won't let the car start and the Engine Failsafe Mode light appears Also the key can be taken out of the ignition and the vehicle won't shut off when on?

This sounds like a problem that is better left to the Jaguar dealer to resolve. The security system and interfaces are extreamly complicated.

Answer

Just happened to my 2001 Jaguar S Type. Problem was the entire electrical system had become wet. Needed a new wire harness, fuse box, etc. etc. etc. The part where the car won't shut off when the key was removed all I had to do is step on the brake and the car shut down.

Not to scare anyone, but it may be a combination of more than one concurrent problem as well:

1) I had a situation when the flooded trunk caused alarm activation, running out of battery and then preventing the start.

2) I had a problem the car forced into a Failsoft mode mode, - but this one was caused by a faulty rear control unit ("computer") in the trunk (located behind a side panel on the gas cap side) - this intermittent failure was forcing the car in the FailSoft mode as well.