非静态方法是GooglePlayServicesAvailable,并且无法从静态上下文引用getErrorDialog

努兰已经指出了正确的答案.

替换您的方法

protected void IsPlayServicesAvailable() {
    int resultCode = GoogleApiAvailability.isGooglePlayServicesAvailable(this);

    if (resultCode == ConnectionResult.SUCCESS){
        msgText.setText("isGooglePlayServicesAvailable SUCCESS");
    } else {
        GoogleApiAvailability.getErrorDialog(this, resultCode, 1).show();
    }
}

通过

protected void IsPlayServicesAvailable() {
    int resultCode = GoogleApiAvailability.getInstance().isGooglePlayServicesAvailable(this);

    if (resultCode == ConnectionResult.SUCCESS){
        msgText.setText("isGooglePlayServicesAvailable SUCCESS");
    } else {
        GoogleApiAvailability.getInstance().getErrorDialog(this, resultCode, 1).show();
    }
}