How do you know it's not a battery issue? A poor connection at the terminals can cause exactly this type of problem. I'd start by removing the terminals from the battery and making sure they, and the posts, are clean. Then put them back and tighten them securely. If the problem persists look for other poor or intermittent connections in the main power and ground wiring.
There is no factory immobilizer in an '02, only a starter kill if it has the optional alarm. The starter kill will prevent the car from cranking but won't do anything to the dash lights so that isn't where the problem is.
The flashing light may be the security light. If so it should be out if the car was unlocked with the remote, unless it's in valet mode in which case it will blink twice and pause, repeatedly.