Lots of errors in your code. Mine is basically the same that @frarugi87's answer.

I only have to add: when reading serial, wait for the end of line ('\r' and/or '\n') to know when you have all your data, so you don't depend on length (which can be corrupted).

String code, rs1, rs2, rs3, readString;
void setup()
{
   Serial.begin(9600);
   Serial.println("Serial ready!");
}

 void loop()
 {
  while (Serial.available()) {
    char c = (char) Serial.read();

    if (c != '\r' && c != '\n') {
      readString += c;
    }
    else {
      rs1 = readString.substring(0, 3); //034
      rs2 = readString.substring(3, 6); //000
      rs3 = readString.substring(6, 9); //017
      code = rs1 + rs2 + rs3;
      Serial.println(code);

      if (code.equals("034000017")) {
        Serial.println("OK");
      }
      readString = "";
    }
  }
}

Lots of errors in your code. Mine is basically the same that @frarugi87's answer.

I only have to add: when reading serial, wait for the end of line ('\r' and/or '\n') to know when you have all your data, so you don't depend on length (which can be corrupted).

Edit (on Majeko's comment)

String code, rs1, rs2, rs3, readString;
void setup()
{
  Serial.begin(9600);
  Serial.println("Serial ready!");
}

void loop()
{
  static bool inData = true;

  while (Serial.available()) {
    char c = (char) Serial.read();

    if (c != '\r' && c != '\n') {
      readString += c;
      inData = true;
    }
    else {
      if (inData) {
        rs1 = readString.substring(0, 3); //034
        rs2 = readString.substring(3, 6); //000
        rs3 = readString.substring(6, 9); //017
        code = rs1 + rs2 + rs3;
        Serial.println(code);

        if (code.equals("034000017")) {
          Serial.println("OK");
        }
        readString = "";
        inData = false;
      }
    }
  }
}

This code works for any configuration of line ending ('\r', '\n' or '\r\n').

It doesn't test for length (or validity or timeout); it's left as an exercise to the reader :-)

I hope it shows how code grows when making it robust in all scenarios.