thanks for your answer! I appreciate your help, and sorry, I didn't want to put xampp in question;-) but I was for a moment insecure.
I get following message on the xampp control Panel v3.2.1
20:51:29 [main] Initializing Control Panel
20:51:29 [main] Windows Version: Windows 8 Pro 64-bit
20:51:29 [main] XAMPP Version: 1.8.3
20:51:29 [main] Control Panel Version: 3.2.1 [ Compiled: May 7th 2013 ]
20:51:29 [main] You are not running with administrator rights! This will work for
20:51:29 [main] most application stuff but whenever you do something with services
20:51:29 [main] there will be a security dialogue or things will break! So think
20:51:29 [main] about running this application with administrator rights!
20:51:29 [main] XAMPP Installation Directory: "c:\xampp\"
20:51:29 [main] Checking for prerequisites
20:51:29 [main] All prerequisites found
20:51:29 [main] Initializing Modules
20:51:29 [Apache] XAMPP Apache is already running on port 80
20:51:29 [Apache] XAMPP Apache is already running on port 443
20:51:29 [main] Starting Check-Timer
20:51:29 [main] Control Panel Ready
20:51:37 [Apache] Attempting to stop Apache (PID: 1384)
20:51:37 [Apache] Attempting to stop Apache (PID: 9388)
20:51:37 [Apache] Status change detected: stopped
20:51:53 [Apache] Attempting to start Apache app...
20:51:53 [Apache] Status change detected: running
20:52:06 [mysql] Attempting to start MySQL app...
20:52:07 [mysql] Status change detected: running
20:52:09 [mysql] Status change detected: stopped
20:52:09 [mysql] Error: MySQL shutdown unexpectedly.
20:52:09 [mysql] This may be due to a blocked port, missing dependencies,
20:52:09 [mysql] improper privileges, a crash, or a shutdown by another method.
20:52:09 [mysql] Press the Logs button to view error logs and check
20:52:09 [mysql] the Windows Event Viewer for more clues
20:52:09 [mysql] If you need more help, copy and post this
20:52:09 [mysql] entire log window on the forums
About Administrator: I am logged in as Administrator, says the Windows Benutzerkonten-information. - Xampp is now running on C:\xampp . Before I had it also in my own folder, in order to be on the good side with administrator rights, but MySQL didn't work either. I even downloaded the TweakUAC-programm and tried it without any restrictions concerning registration-rights, but also negativ.
My last hope is your help and systematic questionary to bring it to work.