@ionic/App-script and other modules missing

I have a project that I started last year, but this year I can't seem to get it up and running.
It says that the ionic/app-script is missing, and if I manually install that, it says Cannot find module angular/tsc-wrapped/src/tsc, which I can't install.

**However, I started the project last year around september, but currently I have the following installed:**

* Node v8.6.0
* NPM v4.3.0
* Ionic v3.12.0
* Cordova v7.0.1

### This is the package.json from the project:

```
{
"dependencies": {
"@angular/common": "2.0.0-rc.4",
"@angular/compiler": "2.0.0-rc.4",
"@angular/core": "2.0.0-rc.4",
"@angular/platform-browser": "2.0.0-rc.4",
"@angular/platform-browser-dynamic": "2.0.0-rc.4",
"@angular/http": "2.0.0-rc.4",
"@angular/forms": "0.2.0",
"es6-shim": "0.35.1",
"ionic-angular": "2.0.0-beta.11",
"ionic-native": "1.3.10",
"ionicons": "3.0.0",
"reflect-metadata": "0.1.8",
"rxjs": "5.0.0-beta.6",
"zone.js": "0.6.12"
},
"devDependencies": {
"del": "2.2.0",
"gulp": "3.9.1",
"gulp-watch": "4.3.5",
"ionic-gulp-browserify-typescript": "2.0.0",
"ionic-gulp-fonts-copy": "^1.0.0",
"ionic-gulp-html-copy": "^1.0.0",
"ionic-gulp-sass-build": "^1.0.0",
"ionic-gulp-scripts-copy": "^2.0.0",
"ionic-gulp-tslint": "^1.0.0",
"tslint-ionic-rules": "0.0.4",
"run-sequence": "1.1.5"
},
"cordovaPlugins": [
"cordova-plugin-whitelist",
"cordova-plugin-console",
"cordova-plugin-statusbar",
"cordova-plugin-device",
"cordova-plugin-splashscreen",
"ionic-plugin-keyboard"
],
"cordovaPlatforms": [
"ios",
{
"platform": "ios",
"version": "",
"locator": "ios"
}
],
"name": "drinkmate",
"description": "drinkmate: An Ionic project"
}
```

_I have NVM and I have tried to run it with earlier versions of Node but without any luck.
What is the issue here and how can I overcome it so I can run my project?_

Start with the package.json and the reported Node, npm, Ionic, and Cordova versions, then reproduce the missing @ionic/app-script and angular/tsc-wrapped module errors. Trace which dependency or project-generation path produces them. Done means the existing drinkmate project installs and starts without either missing-module error.

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