First thing to try is to open your Task Manager via holding down ctrl&alt and pressing "delete" one time. When the manager is open, go to the Process tab and look whether there is a limewire.exe process running. If so, force it to end and then try your installation using the LW offline installer.

If that doesn't work, then you have to do it the hard way.
Try uninstalling LW via START>Programs>LimeWire>Uninstall, if it is still there.
If it isn't just go on with the next step

Use the search function of your computer and look for any remaining LW file using the search query "limewire". Delete all files you can find.

Then go to START>Run and type "regedit" to open your registry. There you go to the "edit" tab and use "find" with the same search query. Delete all registry entries you can find for LW. Then restart your computer and try to make the new installation.

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"Never Argue With An Idiot. They Will Drag You Down To Their Level, Then Beat You With Experience"