How exactly did you uninstall XAMPP as it would seem that perhaps the Apache Windows service may not have been uninstalled first.
It would be advisable to uninstall correctly and do a fresh install by following this procedure.
Start the XAMPP Control Panel.
Make sure there are no ticks in any of the Svc check boxes or the service module column in XCPv3.
Stop all XAMPP components.
Press 'Exit' or 'Quit' in the XAMPP Control Panel.
Delete the xampp folder completely after backing up your own files.
Reboot as it often helps clean things up.
Try and install again using my preferred method instructions below for the ZIP or 7zip version.
Download the ZIP
version of XAMPP.
Extract (drag) the xampp
folder to the C:\ drive or the root of any drive or partition like D:\, E:\, etc.
Run the C:\xampp\setup_xampp.bat
file (this sets the correct paths for you).
Open the XAMPP Control Panel version 3 (xampp-control-3-beta.exe) found in the xampp folder and start Apache and MySQL (do not tick any service module boxes
When both Apache and MySQL are running type http://localhost/
select your language and exercise all the demos in the left menu frame.
You should now be able to proceed and enjoy XAMPP.