2002 XKR with 25,000 miles. Car starts every time, but within 3 seconds the engine stops. Does not run rough. Just goes from smooth start to stop in 3 seconds. Will keep doing the same upon each start up.

Have you tried the spare key? It sounds like an immobiliser problem to me, specifically the system is no longer recognising the key so the spare may well work.

There may be other causes but give the spare key a try first.