Also are you using the SD card? If you are not then it needs to be disabled by setting pin 4 as an output pin and set HIGH in your sketch.
Probably worth doing a firmware upgrade of the board if you haven’t already done so.
Entering http://blynk-cloud.com/auth/project in the browser gives a connection with the server and replacing with the authorisation key
{“id”:1274048251,“name”:“led on/off”,“createdAt”:1486910126,“updatedAt”:1486921948553,“widgets”:[{“type”:“BUTTON”,“id”:866257424,“x”:0,“y”:0,“color”:-1,“width”:2,“height”:2,“tabId”:0,“label”:“led”,“deviceId”:0,“pin”:-1,“pwmMode”:false,“rangeMappingOn”:false,“min”:9,“max”:1,“pushMode”:false,“onLabel”:“ON”,“offLabel”:“OFF”}],“devices”:[{“id”:0,“name”:“ledonoff”,“boardType”:“Arduino UNO”,“token”:“8f9c8e646e0e47f284ec74565dee9dc1”,“connectionType”:“WI_FI”,“status”:“OFFLINE”,“disconnectTime”:0}],“boardType”:“Arduino UNO”,“theme”:“Blynk”,“keepScreenOn”:false,“isAppConnectedOn”:false,“isShared”:false,“isActive”:true}
OK that means you auth checks out, as long as it is exactly the same in your sketch.
SD card?
No I don’t use a SD card.
I added the followingl lines as first lines in setup()
pinMode(4,OUTPUT);
digitalWite(4,HIGH)
Why should is disabled. I didn’t a firmware update ? Is that necessary
Depends how old the firmware is, how many bugs it has and how many improvements have been made since they flashed your board.
Looking at the GitHub at https://github.com/arduino/Arduino/tree/master/hardware/arduino/avr/firmwares it appears the firmware hasn’t been changed for 3 or 4 years.
So unless you have an old shield I wouldn’t bother.
The upgrade procedure doesn’t look that straightforward either.
Perhaps add the following as the first line of your sketch and paste Serial Monitor details:
#define BLYNK_DEBUG
My Wifi Board is 2 years old I think, I was already latest firmware versions are older
added the debug line show only the FREE RAM available, still it doesn’t connect
Nothing else?
Have you used the Shield to connect to other internet services?
All I can suggest is a thorough read through the Arduino WiFi Shield docs at https://www.arduino.cc/en/Main/ArduinoWiFiShield
No I didn’t
I only use the example program of the board, scanning network and that does work without errors
Maybe something with port forwarding in the router ?
The great thing about Blynk is it doesn’t need any port forwarding for their cloud service. In fact that is how I stumbled across them when I first found them. I use a WISP that doesn’t permit port forwarding.
If you have never used the Shield I suspect it’s not quite set up right.
Using the WiFi examples, I created a server.
Pingng from my laptop gives a reply so I think the shield is OK
By the way, which options exist to setup the shield ?
I suspect the baud rate of the Shield is set at a default of 115200 whereas with Arduino’s Blynk requires a much slower speed of 9600 / 19200.
Have you worked out how to send AT commands to the shield?
We might be able to check current rate and then set to 9600.
@JanMenssen the other thing to try is remove BLYNK_DEBUG, BLYNK_PRINT and keep Serial Monitor closed. Your Uno only has one Serial connection and the ESP needs it so you can’t use it for Serial Monitor.
It might mean you have to work blind for now until you hook up a USB2TTL adaptor but you can check in the app if you get connected to the server.
I think I should update the firmware
In the Arduino forum firmware version 1.0.0 is for Arduino IEDE < 1.0.3
and firmware version 1.1.0 is for Arduino IDE > 1.04
Nest step, find the correct firmware version 
@JanMenssen this might help http://katrinaeg.com/arduino-wifi-firmware-upgrade.html
Version 1.1.0 firmware is within the IDE (certainly is for my 1.6.12).
For Windows lcoated at:
C:\Users\username\AppData\Local\Arduino15\packages\arduino\hardware\avr\1.6.15\firmwares\wifishield\wifiHD