You said you have a remote starter, as a 2001 model I assume this is aftermarket, it could be the secondary part of that remote starter that is failing. The remote starter is a stand alone universal unit, so it needs something to talk to the correct system, that piece of equipment is vehicle specific, and those can fail. Sometimes they need to be replaced or sometimes they can get reflashed. I would start by disabling the that remote remote start, especially if it is a few years old