Warrant issued in 2003 for burglary. Never arraigned and did not know of warrant until now. Has statute of limitations run?

The statute of limitations has to do with the time in which charges must be filed.  Since they already have been in your case, there is no defense as to that point of law here.

At this point a warrant for your arrest has been issued.  What you need to do now is to consult with an attorney in the area where all of this happened.  They will best be able to utilize their local contacts for your benefit.  If you ignore this situation and you are stopped for any minor infraction or even have an employment background check, this can all turn up.  At that point, you will be placed into custody.

And know this, it would be far better to turn yourself in then to appear in court courtesy of the jail bus.  At this point you want to take whatever action you can that will be looked at with favor by the court.