OK, I think it may be best if you uninstall XAMPP and start over with a clean default installation as it maybe there is some corruption somewhere hampering our moving forward.
First make sure that there are no ticks in any of the Svc check boxes and all buttons show Start.
Close the XAMPP Control Panel.
Now save all your own files that are in the htdocs folder but don't save any XAMPP files or folders.
Now delete the xampp folder completely.
Re-start your PC to make sure there are no issues with starting your PC.
Next install XAMPP to the root of a drive - I:\ for example and the install script will create I:\xampp do not add xampp or you will get i:\xampp\xampp which although will work is not recommended.
Now run I:\xampp\setup_xampp.bat file and at item 5 select auto for the IPv setting.
Go through and select what you need but do not enable mod_perl item 6 unless you know for sure that your perl scripts need it and most don't need it.
Next run the XAMPP Control Panel and try and start Apache and MySQL before attempting to do anything else as we want to test the default installation.
If you get both to show the green running indication then type in your browser
http://localhost and let me know back what you see and also if you get this far.
Good luck