Try using a different DS Lite AC adapter with the unit if possible. If the unit does function with a different AC adapter, only the AC adapter will be required for inspection by a Nintendo technician. Alternatively should the product be outside of the warranty period a new official AC Adapter can be purchased by contacting Nintendo Customer Service.
If this does not correct your issue, the unit and AC Adapter will both need to be returned to Nintendo Australia for inspection/repair.
NOTE: Only the AC Adaptor from the same model Nintendo DS can be used, eg. If testing for an issue with a Nintendo DS Lite make sure to test ONLY with parts from another Nintendo DS Lite.