Hello!
Try to download and install the latest JRE Applet runner which you can find
Here
Install it and then try to install LimeWire once again and see if it is functional this time if not then you might have to be be logged in as Administrator or Root user in Windows in order for you to install LimeWire.But hopefully this is not the case.If it is then someone here might be able to help you to log in as Administrator or Root users.