When I drive for about 15-20 miles, the speedometer 0-outs and I have no acceleration. The "check engine" light starts flashing. However, the motor does not die. After 10-20 secs., the speedometer starts working and the motor is once again engaged. I replaced the speed sensor. The problem continued. I used an od-2 and the code came back as a defective EGR valve. I replaced that and it seemed like that would solve the problem. However, it did not. Same problem. Even though the "check engine" light comes on, there are no codes to retrieve!? I am baffeled!!! The calais is a 1990 with a Tech-4 engine, with 60,000 original miles.. Any ideas???

If the engine light flashes while driving you could damage the catalyst if it's running poorly.

Could be a transmission problem or something as simple as bad spark plugs.
The engine is under the most load when RPM is low and you are trying to accelerate, such as when it upshifts.
You should have the computer checked for trouble codes and hopefully that will point you in the right direction to test.
If the spark plugs have more than 50,000 miles of wear you might start with replacing them.

The speedometer or the speed sensor are broken. Buy new parts here:
Speedometer:
http://www.woodfins.com/Parts/2008-TOYOTA-YARIS-83-R119-273-Speedometer_Instrument_Cluster.html

This could be something as simple as a misfire or you could have killed your ******. Was the check engine light flashing when this was happening

You need a professional mechanic with a scanner. Never drive a car with a flashing check engine light except to get it off the road. Flash = serious issue.

2005 BUICK LESABRE TACHOMETER DOES NOT REGISTER WHEN ENGINE IS RUNNING. SOMETIMES IT BARELY MOVES, THEN GOES BACK TO 0
SAME CAR HAD SPEEDOMETER QUIT, REPLACED WITH NEW SENSOR, DROVE ABOUT 1300 MILES AND IT QUIT AGAIN. CLEANED THE SENSOR, WORKS OK NOW.

check your wheel speed sensors. and vehicle speed sensor on the transmission

drive 4 uses it to sense slip in the front/rear wheels.

check engine light on because it needs to know vehicle speed to shift properly.

no speedometer because it turns the voltage into a signal to the gauge

You need to replace the vehicle speed sensor located on the trasmission.

the check engine flashing means the engine is misfiring and can cause catalyst damage ,have it looked at right away,lots of problems with ignition coils and ignition wires causing misfires

First off, I have a 1987 Supra non-turbo and I have seen a similar problem on my car. Probably one part of the two part speedo cable has broken, or the speed sensor has failed. The speedo cable turns a speed sensor which is part of the speedo gage cluster. The signal right now from the speed sensor to the computer is probably zero so the PCM thinks the car is stopped. The PCM has a limit on how high the engine will rev while the car is not moving. This is also the "limp home mode" max rpm in case the speed sensor fails. So if you fix your speedo/speed sensor, I think the acceleration problem will go away. The cable is in two parts--a "lower cable" which goes from the tranny to a junction and an "upper cable" which goes from the junction to the speedo. You will need to determine which cable is broken or if the speed sensor itself has a broken part.

To check the cable, find the junction under the car on the passengers side and disconnect it. The cable frequently breaks right at this spot. You will be able to turn the upper speedo cable by hand and have a partner listen/look for results on the speedo cluster. If the cable checks out, you may have to pull the instrument cluster to check what is wrong with the speed sensor.

Secondly, the flashing O/D light is signaling you that there is a trouble code waiting (probably for the transmission which also needs a speed signal). You can obtain trouble codes from the PCM via the diagnostic connector in the engine compartment. The connector is on the driver's side of the compartment just behind the fuse box. It is labeled "diagnostics". Using a paper clip or a hair pin and a jumper wire, connect the terminals "T" and "E1". (there is a guide to the terminals on the inside of the plastic flip cover.) Turn the ignition to on but do not start the car. The check engine light will start flashing two digit codes. (Four flashes followed by two flashes=Code 42= speed sensor signal lost.) There will be a pause then the next code. At the end of the codes, it will start repeating the sequence of codes again until you turn off the ignition. If there are no codes, the check engine light will just flash continously once every second. Don't forget to remove the diagnostic jumper before starting or driving the car.