There are times when XAMPP will install, all will look OK, but it's Apache module just won't start. You click on the "Start" button, it starts, then stops. Click again: the same. No pop up error messages, no nothing. The problem, most often is that some other program is already using the same ports.
I have seen when IIS is using them, other programs. But, most often, it's the Skype, you are using.
If it's Skype, just open it, click on:
Tools -> Options -> Advanced -> Connection