problems installing the new version for flash
in Library/Internet Plug-ins, nothing appears when running the installation nor when the installation is complete
What do you mean by "installing from another account?
Are you looking in the correct library? The one it should appear in is at the top level of the root folder, the hard drive folder, not your home folder library.
If it still doesn't show, try installling again from Safe Boot. Hold Shift down at the startup chime and expect a much longer boot.
Only get Flash Player here.