The reason you aren't getting any error messages is that all the code you have written is legal. When your code is legal and there is no run time error, then you need to start thinking about logic errors.
The above snippet means that if user enters a value > 9 the while loop will end, and the value of newnum will be ignored, not pushed on to stack. If you want to allow all values to be entered on to stack and then remove any value user has entered that is larger than 9, that's a different series of steps. Your code prevents the need to remove anything greater than 9, because those values aren't pushed in the first place.
cout<<"enter a digit\n";
In your Peek function you only allow peeking at the top value of the stack. You don't ask to look lower down. To do so would require additional code, and I think it would violate the spirit of using a stack to begin with, but it can be done. To look further down you would need to pop the top and store it in another, temporary stack. That way you can keep track of all the values peeked at. When you are done peeking you can pop the values off the temporary stack and push them back on the original stack. As you are peeking, if you don't like a value you can remove it from the original stack by not pushing it on the temporary stack. The problem is I think of peeking as looking and replacing, but not removing. If you remove, you intervene, not just peek.