2005 S40 has electrical / ignition issues

[Numbersguy]

My step daughter bought a 2005 S40 and now it is having electrical problems. Sometimes it does nothing when she puts the key in and tries to start it. Sometimes the dash lights and accessories stop working while the car is running. After 10 minutes of trying to start the car last night the dash lights and the lights on the center console began blinking on and off without the key in the ignition. The dealer she bought it from has replaced the battery and the main relay switch.

Any ideas on what this is caused by?