The reason we ask for your OS version and the XAMPP version is because we have found that the best support we can offer is now version related.
XAMPP 1.7.5> versions have been compiled with VC9 2008 and so they are different to earlier version (VC6) and are very much Windows version reliant that the correct runtime files are present, among other strange anomalies that this forum is seeing on a daily basis.
XAMPP is a suit of components ported from Linux, not a single piece of software, so each individual component needs to be tuned to each and every version of Windows by the use of configuration files.
If you do an Internet search for your exact MySQL error 1042 message then you will see that there is no definitive solution even from MySQL Dev and it is not limited to only Windows computers but also to any OS that MySQL will run on.
On these forums we do manage to solve 99% of support request in both English and German language forums and in other operating systems, that's our record of success over the many years the XAMPP suit of components has been released and the millions of successful installations.
So your next step is to try and tune the individual component's configuration files to suit your particular computer.
The help already provided here, no matter how inadequate, was based on the details you have provided and on previous solved issues, so if you omitted some details then perhaps the help offered was not relevant.
I can't see that there is any more help that can be offered except to say that the XAMPP Lite version is just that and perhaps you may like to try the full version to see if that works for you, and if it does then obviously the lite version is not for you (the full version zip or 7zip unpacks to removable media as long as you don't run the setup_xampp.bat file - IZArc is not recommended to unpack 7zip files: viewtopic.php?f=16&t=48955