Corrected Version
var inputEl = document.getElementById("inputID");
unction myFunction() {
  if (inputEl.value === 'Hi') {
    alert("Hello");
  } else {
    alert("Goodbye");
  }
}
Which is pretty much what you had, except for few fixes and best practices:
- the variable name change (inputElinstead of1- see Valid Identifiers below)
- the strings in the alertstatements (maybe they were variables, but we couldn't assert it from your snippet);
- the strict equality comparison;
- the missing semi-colons;
Why It Didn't Work
It doesn't work because of the 1 variable name being invalid.
Then if it still doesn't work after that, then your HTML is wrong and the ID of your element isn't really inputID,
Valid Identifiers
if you try this in Chrome's console (or another JS environment) to replicate your variable declaration:
var 1 = 'test';
You'll get a nice output similar to:
SyntaxError: Unexpected number
So, just changing your variable name should be enough, if there aren't any other issues.
FYI, According to the Mozilla Developer Network, valid identifiers in JavaScript are:
A JavaScript identifier must start with a letter, underscore (_), or
  dollar sign ($); subsequent characters can also be digits (0-9).
  Because JavaScript is case sensitive, letters include the characters
  "A" through "Z" (uppercase) and the characters "a" through "z"
  (lowercase).
Starting with JavaScript 1.5, you can use ISO 8859-1 or Unicode
  letters such as å and ü in identifiers. You can also use the \uXXXX
  Unicode escape sequences as characters in identifiers.
For a less digestable version, the full spec for identifiers is in the 5.1 Edition of the ECMA-262 standard in section 7.6