My left front door won't open with the outside handle. Upon inspection, it appears that a rod has become dislodged from the inside mechanism. How do we reinstall it.

Their is a rod that runs from inside handle to a lever that pulls up on the latch mechanism. The outside handle has a rod that runs to the same place, what I have seen is the rod running from lever to mechanism come loose at the mechanism and neither handle will work.

There is a rod inside the door that connects the inside and outside door handles to the latch mechanism, if it gets bent or broke it won't activate the latch. The inside door panel will have to be removed and parts of the mechanism also to reinstall. Would recommend maybe taking somewhere unless it's an old BWM.

There is a rod linkage that connects the outside door handle to the latch mechanism. You will have to take the door panel off and inspect the rod.

The outside door handle may be broken or may have become disconnected from the rod that allows the door to open. Sometimes the ther is a plastic clip that connects the rod to the door handle and could be broken any parts store will have replacement clips. Whatever the problem is, the door panel will have to be removed to be able to inspect the condition of the door handle and parts attaching to it.

In all probabilty, the metal rod that runs from the outside handle down to the locking mechanism has become dislodged. This same rod also operates the inside door handle. Either that, or one of the plastic connecting levers to the same rod has broken. For this repair you will have to dismount the inside panel of the door. Search in this site for the steps to disassembling the panel. I think i wrote about it once.

inside the door on the release mechanism there are two rods held to the lock assembly by nylon clips. One is activated when you open the door from the inside the other from the outside. It sounds like one of the nylon clips has broken or come loose. This often happen after someone has locked their keys in the vehicle and used a slim jim to open the door.(a slim jim is a long flat piece of metal used to trip the lock from outside by inserting it between the window and the weatherstrip and activating the rod) Often during this process the rod is dislodged from the slot in the lock mechanism.

To access this you must first remove the inside door panel and the moisture barrier. You can then see if the rod is loose and if the clip is broken or just knocked loose. On some vehicles it's not possible to actually see the lock assembly and you have to feel your way through the process of checking for a broken clip or a loose rod.

Had the same problem happen to me on a rear door. A mechanic lowered the window, and managed to "fish" the metal rod that goes from the outside handle down to the locking mechanism. Usually, this rod becomes dislodged at the top end, where it meets the outside and inside handle rods, disabling both. If it became dislodged at the bottom, where it meets the locking mechanism, then this procedure will not work. Much of the front door panel can be disassembled with the door closed. And maybe, just maybe, if you take out the window switches sub panel from the door panel, you will be able to look for and reach the rod actuator. This subpanel (black plastic) is held by just two screws at the bottom, hidden with a plastic top, that you have to pry out to reach the screw itself.

It sounds like the plastic connecting bit that links the outside door lever to the rod, that operates the door mechanism, has broken or become disconnected. To check, you will need to remove the trim on the inside of the door, after removing any screws and the inside door lever. However now that the child safety lock has been set it could be very difficult to get the door open.
All I can suggest is that you look at the other rear door to locate the position of the safety tab and then try to disengage it by using a suitable thin blade or something on your bad door so that you can again use the inside lever.
Once you have the inside trim off and the plastic sheet, you will see an access hole for the door mechanism and the outside operating handle of the door. It should be attached to the actuating rod by the aforementioned plastic bit. If plastic bit appears OK try re-attaching it or replacing it if broken. If the part of the handle which attaches to the rod is broken, the handle will need replacing.

The lock / unlock operations are performed either electrically or manually directly on the solenoid installed on each door, and has nothing to do with the opening mechanism. In all probability, the metal rod that goes up from the door latching mechanism to the outside and inside handle, has become unattached / dislodged from the unit. This requires taking down the inside of the door panel, in order to reach the latch, and its operating rods. Look elsewhere on Fixya, for instructions on how to dismount the door panel. I think i provided instructions for this in the past.

You will need to remove the inside door trim panel and check the three (3) rods and plastic connectors that connect:
(a) the inside door handle to the door mechanism
(b) the inside door lock knob/outside key lock cylinder to the door mechanism
(c) the outside door handle to door mechanism.

Most likely one (or more) of these rods have either become loose or the plastic lock clips have broken.
The "L" end of the rod goes thru the hole of the clip and the clip has a pivoting "U" shape that goes over and locks onto the rod.
Based on the your year (2000) it might be a good idea to remove all clips and rods; and remove the entire door mechanism. Inspect, clean, lubricate, and re-install it.