I have followed the Tutorial. After changing app/maint.ts in the Http chapter I get the error when starting the app via command line: 
ap
I encountered a similar problem. I just downloaded the entire example near the end of part 7 (last part) of the tutorial and ran it. It worked.
Of course, you need to install and compile everything first.
> npm install
> npm start
I also changed 'app-root' to 'my-app' in app.component.ts.
As of latest (currently 0.1.14), this is what's stated in the CHANGELOG
In
systemjs.config.jsyou should change the mapping to:'angular-in-memory-web-api': 'npm:angular-in-memory-web-api/bundles/in-memory-web-api.umd.js'then delete from
packages:'angular-in-memory-web-api': { main: './index.js', defaultExtension: 'js' }
in app\main.ts simply modify:
import { InMemoryBackendService, SEED_DATA } from 'angular2-in-memory-web-api';
to:
import { InMemoryBackendService, SEED_DATA } from '../node_modules/angular2-in-memory-web-api';
then add the index.js parameter in
var packages = {
    'app': { main: 'main.js', defaultExtension: 'js' },
    'rxjs': { defaultExtension: 'js' },
    'angular2-in-memory-web-api': { main:'index.js', defaultExtension: 'js' }
};
in systemjs.config.js
it's work for me.
It works for me:
In package.json dependencies block set ( use "angular" instead of "angular2")
"angular-in-memory-web-api": "^0.3.2",
Then run
 npm install
OR
simply just run (my preferable)
npm install angular-in-memory-web-api --save
If you are using angular cli, you would get this error.
Please add 'angular2-in-memory-web-api' in the const barrels in the system-config.ts file as below:
 const barrels: string[] = [
  // Angular specific barrels.
  '@angular/core',
  '@angular/common',
  '@angular/compiler',
  '@angular/forms',
  '@angular/http',
  '@angular/router',
  '@angular/platform-browser',
  '@angular/platform-browser-dynamic',
  // Thirdparty barrels.
  'rxjs',
  'angular2-in-memory-web-api',
  // App specific barrels.
  'app',
  'app/shared',
  /** @cli-barrel */
];
And add 'angular2-in-memory-web-api': 'vendor/angular2-in-memory-web-api' as below. 
System.config({
  map: {
    '@angular': 'vendor/@angular',
    'rxjs': 'vendor/rxjs',
    'main': 'main.js',
    'angular2-in-memory-web-api': 'vendor/angular2-in-memory-web-api'
  },
  packages: cliSystemConfigPackages,
});
Rebuild using npm start.  This resolved the issue for me.
Changing this line, as suggested above, worked for me in the Angular 2 Heroes Tutorial:
'angular2-in-memory-web-api': { main: 'core.js', defaultExtension: 'js' },