2004 Toyota Land Cruiser starts up but then dies. dealer says it's key issue?

After a recent car wash our 2004 Toyota Land Cruiser would start up but
then die within 1-2 seconds. Both the check engine light and the battery
light came on.  We had it towed 5-6 hours later to the dealership. The tow
person said it started right up and he could drive it into the dealer. The
dealer looked at it and said it was a key issue and that the immobilizer was
bad. So we ordered a new key and immobilizer. The first few days after we
got it back from the dealer, I would have to start it 2-3 times before it would
stay running. It was fine until the next car wash, when it did exactly the
same thing. Drove it home from the car wash and after parking it in the
garage it would start up but then die 2 seconds later. Finally, after letting it
sit in the garage and trying to start it for 48 hours it stayed running enough
to drive it to back out to dealer. They still keep saying the computer says i
has to do with the key??? HELP!