Changing modes with one touch button; on-mode1-mode2-mode3-off-on-mode1, etc.

Hi Janniche,

First off, looking at your schematic you don't seem to have any resistors to limit current to the LED's and driving 5x LED's from one I/O pin will probably draw to much current and damage your LilyPad.

The code you supplied has a few errors like extra void loop() and spurious extra { and } brackets. You have a button in the schematic but don't read it in your main loop to increment buttonPushCounter, you just continually increment buttonPushCounter so it will quickly go from 0 to 1 and 2 then beyond that you don't check for any more states.
Push buttons become very unresponsive when you use long delays in the code as you have.

void loop(){
    if (digitalRead(pushbutton) == HIGH){
        delay(20); // button debounce
        buttonPushCounter++;
        if (buttonPushCounter > 2){
            buttonPushCounter = 1;
        }
    }
    Serial.println("on");
    Serial.print("number of button pushes:  ");
    Serial.println(buttonPushCounter, DEC);
    
    if(buttonPushCounter == 1) {
        digitalWrite(shoulder, HIGH);
        digitalWrite(back, HIGH);
        digitalWrite(frontdown, HIGH);
        digitalWrite(fronttop, HIGH); 
    }
    
    if(buttonPushCounter == 2) {         
        digitalWrite(shoulder, HIGH);
        digitalWrite(back, HIGH);
        digitalWrite(frontdown, HIGH);
        digitalWrite(fronttop, HIGH);
        delay(500);                // wait for 0,5 second
        digitalWrite(shoulder, LOW);
        digitalWrite(back, LOW);
        digitalWrite(frontdown, LOW);
        digitalWrite(fronttop, LOW);
        delay(500); 
    }
}