Today I have finally got my working Limewire !
I followed your instructions :
- I had 3 versions of Java in my browser, which 3 I removed;
- Then, I downloaded the Java 1.5 (JRE), + or less offline ( I think I did it online),
- With the "search" option, I have been able to find the folder called .limewire : it was in my recycle bin, after I had removed at a previous time all my Limewire which didn't work.
- At this time I have downloaded the beta version for Limewire, and miracle, it works nicely!

MILLIONS THANKS TO LORD OF THE RINGS!