A slightly different version of the halting problem
I won't give you the solution - I think you're on the right track. However I will give a possible way of making this question precise:

Prove that this problem is undecidable:


Input: A (code for a) Turing Machine $M$
Output: $\texttt{Accept}$ if the number of inputs for which $M$ halts is a finite number $\leq n$
$\texttt{Reject}$ otherwise.


Since there are an infinite number of inputs, if $M$ halts for a finite number of them, then it doesn't halt for an infinite number of them.

Of course, it's possible for a machine to halt on an infinite number of inputs, and not halt on an infinite number of inputs (say, halt on even numbers and not on odd numbers). In this case, a hypothetical machine for this problem would $\mathtt{Reject}$.

You might notice some similarity to the halting problem at this point.