What's up with my Saturn door locks?

Some times the security system/door locks operate perfectly fine and other times the remote does nothing. In addition the dash lights blink repeatedly for no known reason. The two (the lights and the remote) seemed linked because when the remote is keyed the dash lights blink in response. You'll start the engine and the dash lights and only the dash lights, start blinking at about once a second and continue for minutes. Also if you are sitting at an idle with the transmission in park and try to unlock the doors to get out the doors lock again immediately. I've tried disconnecting the battery for a few minutes and reconnecting it----nothing. I have also put new batteries in the remotes-----again, nothing. It's a 2003 L200.