What would cause stereo system sound to go out when door chime went out?

The door chime is sent through the stereo system, the chime comes out through the driver side speaker.

Chimes are generated by the radio. Unplugging the radio and then plugging it in can activate the security feature in the radio and is very unwise. You can try resetting it by disconnecting the negative battery wire, then plugging the radio in and reconnecting the battery wire. If that doesn't work, check with a dealer to see if they can reset it, but if the radio has been damaged by what you are doing, you may have to replace it.

did you check speaker wires if you have got them wired up right ???

In most vehicles the "chime" is located in the dash around where your 4 way flaser is. It could simply be the door switch also which is a little button that depresses when you close the door to open the circuit shutting the dome light and chime off. They are easy to change and inexpensive. Hope that helps.

Sometimes the ignition key does not "deactivate" when removing the key...try wiggling the washer behind where the key goes...sometimes this sticks...:)

take it to an automotive stereo shop and have them diagnose the system, including the keyless entry.
Good Luck

Section 13-09: Gauges, Warning Devices — Chime System 1996 Windstar Workshop Manual
DESCRIPTION AND OPERATION Warning Chime Systems Three distinct sounds are used to indicate the area of concern. Seat belt warning generates 1 chime per second
key-in-ignition generates 2 chimes per second
headlight on generates 4 chimes per second.
Key-In-Ignition Warning The key-in-ignition warning will sound when the driver's front door (20125) is opened with the key in the ignition switch. It will continue to sound until the key is removed, the front door is closed, the ignition switch is turned to START or the vehicle speed is over 24 kmh (15 mph).

Safety Belt Warning When the ignition switch is turned to RUN or START from OFF or ACC, the chime will sound for six seconds or until the safety belt is buckled.

• The safety belt warning indicator lamp (10C859) will activate for 60 seconds or until the driver's safety belt is fastened. Both the chime and lamp activate at the same time.

Anytime the ignition switch is released from START and returns to RUN while the safety belt lamp or chime is activated, the safety belt warning lamp or chime will remain activated until either the timing sequence has been executed, or the safety belt is buckled.

Headlamp Switch On Warning The chime will be activated if the headlamps or parking lamps are ON, the key is not in the ignition and the driver's door is opened. The chime will sound at a rate of four per second.

This is basically the door chime that stays on. I had the same problems in a couple Ford trucks. the only easy solution it to find where the chime speaker is on your expedition and disconnect it. It should be somewhere behind where your stereo is.

battery needs charged/replaced....charging system needs tested... and you may have had this all caused by a parasitic leak ( electrical draw/drain) that needs to be found