Well, my lampp stated at startup that another mysql was running, and it persisted saying that even though I made sure that no other mysql is up ?
After running around in circles for a while I finally got to read some startup scripts, and afterwards looked under the var/mysql/ folder (that 'var' is a sub-folder located inside the LAMPP_HOME folder, not the system's /var folder which is located directly under the / of the filesystem).
There I searched for a filename 'your-hostname.pid' (that is xxxx.pid, yes?)
and having found it - I deleted it.
And then everything was back to normal...
I'm documenting this because ofr some reason or another, I couldn't find this documented elsewhere. Either it is a strange lampp bug, and I'm to blame for using a relatively old version (mainly for an old internal software), or it is something that expert mysql dbas have another solution for. Go figure. But this worked for me....