Tinker with it. If you can find one of the following and repair it yourself, you'll save a lot of money and narrow the problem that someone else needs to find if your efforts do not yield a working overdrive.
Most likely it is a bad relay, broken wire, corroded electrical terminal, bad solenoid or out of adjustment kick down cable. But first, check fuse number 11. Actually roll the fuse in the clips to clean any corrosion off the ends of the fuse and clips. If the fuse is blown, this points toward a broken wire to the transmission OR since the fuse is also for the rear window defogger grid, a problem with that circuit. The bad circuit for the rear window is more common in wagons than sedans. The wire breaks inside the wagons tailgate hinge.
Does the dash light arrow go on and off when you push the button on the side of the shifter? The orange arrow pointing up is one of the warning lights along the bottom of the instrument cluster toward the right side.
If there is no orange light on all the time or turns on and off when you push the button, look at the fuse, or the light has been removed or burned out. I have seen the light taken out by less than reputable used dealers and private owners who have been told that the only cure for no overdrive is a rebuilt or replaced transmission. Needing to replacing the transmission for no overdrive is as likely as getting hit by lightening. Very unlikely.
If the arrow is on all the time, the relay has a problem internally. Most likely a poor solder joint that can be a home repair if you are good with a soldering iron. Post back for more details if that is the case.
A broken wire is a little bit harder to locate. Most common areas for breaks are where the white wire passes through the front of the cup in the transmission tunnel that holds the shift lever. This wire commes out of the cup above the transmission, drops to a clip on the right rear of the transmission, then lays on top of the transmission as it is routed to another clip on the front left of the transmission before it enters the top of the control solenoid on the left side of the transmission. Somewhere in this route is a connector. This connector gets corrded to the point where no electrical contact is present. While you are down there looking at the wire, separate and clean this connector.
At the top of the solenoid on the left side of the transmisison is another place the wire breaks. If the wire is broken inside the solenoid, it probably is better to get the solenoid replaced. If you want to remove the solenoid to make a repair easier, it is VERY important to have the area around the solenoid VERY VERY clean prior to removing the solenoid. The solenoid sits on a shelf on the side of the transmission and collects not only dirt and grime but small rocks. Allow one of the small bits of rock or grit into the transmission and you will need a costly transmission repair. The space between the solenoid and the trasmission case needs to be cleaned out as well. Brake cleaner after an initial cleaning and wiping with rags helps. Be carefull with the brake cleaner. Wear eye protection and work when the transmission is cold to the touch.
The solenoid also fails electrically. Best way to test is find the connector in the wire mentioned previously, separate it, then with another piece of wire connected to the positive battery terminal, connect the "new" battery wire with the solenoid wire. The solenoid should click each time the wire is connected or disconnected. No click, bad solenoid or bad wire to the solenoid. The solenoid is not cheap, unless it is the wire and you can repair it, but a lot less than another transmission.
An out of adjustment kickjdown cable is another common problem. An indicator that points toward this is late shifts from one gear to another. Normal shift points are 10 to 15 mph, 20 to 25 mph, near 30mph. Overdrive if present is about 40mph. All these are for light acceleration.
Look at the cable where it comes out of the sheath near the throttle. The cable is the one that comes up from the transmission and aligns with the bottom of the throttle drums. At rest the button should be about .25 to 1 mm from the sheath. When the accelerator pedal is fully depressed, the distance to the button should be about 51 mm. DO not turn the throttle drum by hand for this check. Use the pedal. The cable should also slide freely in and out. This you can check using your hand on the cable itself. Pull out about 25 to 40 mm and release. The cable should move freely and return freely without binding. Adjsuting the cable is fairly easy where replacement requires work inside the transmission.
Duane