Não consigo compilar meu código

Carol, cole seu código do webpack config e o seu package.json aqui.

webpack.config

var path = require('path')
var webpack = require('webpack')

module.exports = {
  entry: './src/main.js',
  output: {
    path: path.resolve(__dirname, './dist'),
    publicPath: '/dist/',
    filename: 'build.js'
  },
  module: {
    rules: [
      {
        test: /\.css$/,
        use: [
          'vue-style-loader',
          'css-loader'
        ],
      },      {
        test: /\.vue$/,
        loader: 'vue-loader',
        options: {
          loaders: {
          }
          // other vue-loader options go here
        }
      },
      {
        test: /\.js$/,
        loader: 'babel-loader',
        exclude: /node_modules/
      },
      {
        test: /\.(png|jpg|gif|svg)$/,
        loader: 'file-loader',
        options: {
          name: '[name].[ext]?[hash]'
        }
      },
      { test: /\.css$/, loader: 'style-loader!css-loader' },
      { test: /\.(woff|woff2)(\?v=\d+\.\d+\.\d+)?$/, loader: 'url-loader?limit=10000&mimetype=application/font-woff' },
      { test: /\.ttf(\?v=\d+\.\d+\.\d+)?$/, loader: 'url-loader?limit=10000&mimetype=application/octet-stream' },
      { test: /\.eot(\?v=\d+\.\d+\.\d+)?$/, loader: 'file-loader' },
      { test: /\.svg(\?v=\d+\.\d+\.\d+)?$/, loader: 'url-loader?limit=10000&mimetype=image/svg+xml' }
    ]
  },
  resolve: {
    alias: {
      'vue$': 'vue/dist/vue.esm.js'
    },
    extensions: ['*', '.js', '.vue', '.json']
  },
  devServer: {
    historyApiFallback: true,
    noInfo: true,
    overlay: true
  },
  performance: {
    hints: false
  },
  devtool: '#eval-source-map'
}

if (process.env.NODE_ENV === 'production') {
  module.exports.devtool = '#source-map'
  // http://vue-loader.vuejs.org/en/workflow/production.html
  module.exports.plugins = (module.exports.plugins || []).concat([
    new webpack.DefinePlugin({
      'process.env': {
        NODE_ENV: '"production"'
      }
    }),
    new webpack.optimize.UglifyJsPlugin({
      sourceMap: true,
      compress: {
        warnings: false
      }
    }),
    new webpack.LoaderOptionsPlugin({
      minimize: true
    })
  ])
}

package.json

{
  "name": "Projeto X",
  "description": "Projeto X",
  "version": "1.0.0",
  "author": "Carolina Cruz",
  "license": "MIT",
  "private": true,
  "scripts": {
    "dev": "cross-env NODE_ENV=development webpack-dev-server --open --hot",
    "build": "cross-env NODE_ENV=production webpack --progress --hide-modules"
  },
  "dependencies": {
    "bootstrap": "^3.3.6",
    "vue": "^2.5.11"
  },
  "browserslist": [
    "> 1%",
    "last 2 versions",
    "not ie <= 8"
  ],
  "devDependencies": {
    "babel-core": "^6.26.0",
    "babel-loader": "^7.1.2",
    "babel-preset-env": "^1.6.0",
    "babel-preset-stage-3": "^6.24.1",
    "cross-env": "^5.0.5",
    "css-loader": "^0.25.0",
    "file-loader": "^1.1.4",
    "style-loader": "^0.13.2",
    "url-loader": "^0.5.9",
    "vue-loader": "^13.0.5",
    "vue-template-compiler": "^2.4.4",
    "webpack": "^3.6.0",
    "webpack-dev-server": "^2.9.1"
  }
}

No webpack config, a regra para aplicar os arquivos CSS esta sendo aplicada duas vezes.

Aqui

{
        test: /\.css$/,
        use: [
          'vue-style-loader',
          'css-loader'
        ],
}

e aqui

      { test: /\.css$/, loader: 'style-loader!css-loader' },

Isso acontece pq a versao do template webpack-simple que vc está usando ja deve ter vindo com essa etapda configurada. =)

Sim, acabei de verificar isso no código. Fiz os acertos e agora funcionou. Obrigada pela ajuda.