I recently wrote a short algorithm to calculate happy numbers in python. The program allows you to pick an upper bound and it will determine all the happy numbers below it.
I can see that you have quite a few heap allocations that are unnecessary
For example:
while(!next)
{
char* buffer = new char[10];
This doesn't look very optimized. So, you probably want to have the array pre-allocated and using it inside your loop. This is a basic optimizing technique which is easy to spot and to do. It might become into a mess too, so be careful with that.
You are also using the atoi() function, which I don't really know if it is really optimized. Maybe doing a modulus 10 and getting the digit might be better (you have to measure thou, I didn't test this).
The fact that you have a linear search (inVector) might be bad. Replacing the vector data structure with a std::set might speed things up. A hash_set could do the trick too.
But I think that the worst problem is the string and this allocation of stuff on the heap inside that loop. That doesn't look good. I would try at those places first.