I had the same issue and I was also unable to fix my issue. I researched on it a lot and found the below solution on it
1.I had installed the node.js version 8.1.3
2.After that I used the below command to install the npm 5.1.0
npm install npm#latest –g
3.After that I used the below command to install typescript 2.4.1
npm install -g typescript
4.After that I ran tsc --init in my directory. It created the tsconfig.json file in my directory where I was able to define my configuration. VSCode also started using the file once it found it in my root directory.
5.After that I could see my TS version, and was also able to compile the TS code.
Hope it helps you too.