Laptop image Distorted, when connected to external monitor image again normal. What could it be?

On my Sony VAIO laptop, the picture is distorted. When I connect the laptop to one
External monitor connect the picture is normal.
can I exclude a defective graphics card? What could it be?

Do your laptop screen and external monitor have the same format? If not, the laptop screen adapts to the monitor.

When I put the laptop on one

External monitor connect the picture is normal.

can I exclude a defective graphics card?

No, you can't, because:

The video card of your laptop is defective and not the one of the external monitor
Your picture jerks / verpixelt on the laptop

Go with your laptop to a shop for computer science, or to a PC sale. There you can help you the best!

Alternatively, you can sometimes look at the internal Windows program "DxDiag":

Press simultaneously the keys "Windows" and "R", enter into the input field "dxdiag" and click on "OK".
Wait a moment for the program to load completely and then click on the "Display" tab at the top.

The video card of your laptop is defective and not the one of the external monitor

A monitor has no graphics card, everything runs on the laptop graphics card.

In this respect, the FS can pretty well rule out a graphics card defect.

Otherwise, @CarlCraft has pointed the FS to the most likely solution.