How to make JavaScript code more bullet-proof?

I come from a compiled-language background (C/C++/Objective-C) and am currently writing a full-fledged application in JavaScript. (TypeScript actually, but my question is the same for both.)

The problem I'm running into is that if a single error occurs, the entire flow of execution halts. For instance, if I have:

myFunction()
{
    doSomethingA();
    doSomethingB();
    doSomethingC();
}

then if doSomethingA() has something like this:

var myValue = window.myData.myValue;

but "myData" doesn't exist on "window" at the time, then all code STOPS EXECUTING... doSomethingB() and doSomethingC() do not execute, and a console error is logged. That might be fine for simple web pages, but I'm creating an application, and it needs to not 'stop working' inexplicably.

Granted, I can use try/catch to be 'aware' of this error, but that STILL doesn't solve my problem: I would like to write the code in a way such that doSomethingB() and doSomethingC() continue to execute, even if a problem arises. However, this is a huge over-simplification of my code. Imagine there are MANY of these functions. It would be impractical to surround each with its own separate try/catch block. Even if I did, I need the rest of a given function to continue to execute even if something in the first part fails.

Of course, I can 'protect' my variables by using:

if ( typeof window.myData != "undefined")

or

if (window.myData.hasOwnProperty("myValue")

but that becomes very messy if you have several levels to check, such as when accessing:

var myValue = window.myData.something.anotherLevel.somethingElse.value;

Now I have to check if myData, something, anotherLevel, and somethingElse are all valid before accessing this value 'safely'. This results in very ugly code.

Is there a better way to make my code more 'bullet-proof'? If a property is unexpectedly missing, I need code to continue executing after the problem statement. Is that possible without 'protecting' every single statement that accesses data that has even a tiny chance of being undefined?