When driving the car the speedomator goes to 0 and then the tranmission starts slipping

There's a possible worn out clutch inside of the auto transmission. The speedometer going to zero could be the transmission not sensing speed, and then disengaging the transmission to keep the car from stalling at a stop sign, maybe.

Try looking at the VSS (vehicle speed sensor) circuit on the transmission.

Here are some tests that can be performed on the VSS:

A speed sensor. Courtesy of General Motors Corporation, Service Technology Group.
A defective vehicle speed sensor may cause different problems depending on the computer output control functions. A defective vehicle speed sensor (VSS) may cause improper converter clutch lockup, improper cruise control operation, and inaccurate speedometer operation.

• Prior to VSS diagnosis, the vehicle should be lifted on a hoist so the drive wheels are free to rotate.
• Backprobe the vss output wire and connect the voltmeter leads from this wire to ground.
• Select the 20-volt AC scale on the voltmeter.
• Then start the engine.
• Place the transaxle in drive and allow the drive wheels to rotate. If the VSS voltage signal is not 0.5 volt, or more, replace the sensor.
• When the VSS provides the specified voltage signal, backprobe the VSS terminal at the PCM and repeat the voltage signal test with the drive wheels rotating.
• If 0.5 volt is available at this terminal, the trouble may be in the PCM (powertrain control module).
• When 0.5 volt is not available at this terminal, turn the ignition switch off and disconnect the wire from the VSS to the PCM.
• Connect the ohmmeter leads across the wire. the meter should read zero ohm.
• Repeat the test with the ohmmeter leads connected to the VSS ground terminal and the PCM ground terminal.
• This wire should also have zero ohm resistance. If the resistance in these wires is more than specified, repair the wires.
• The condition of a speed sensor can be checked by going through the diagnostic routines for the system.
• If this test indicates that a sensor is faulty, the sensor should be replaced.
• Speed sensors can also be checked with an ohmmeter. Most manufacturers list a resistance specification.
• The resistance of the sensor is measured across the sensor's terminals.
• The typical range for a good sensor is 800 to 1400 ohms of resistance.