Remove your current version of Java & reinstall JRE using the offline installer (point 1 below)
Fixes for LimeWire

If necessary, then reinstall LW using the offline installer.

If that doesn't work, try deleting the LW preferences folder & also changing compatibility... instructions for these are in the thread above

There was no limewire folder in my Application Data. Could this be my problem? If so, how do I solve it?

Thanks in advance.

If it is really so that there was no " LimeWire " folder in your hidden Application Data Folder, I'd recommend you uninstalling LW and your Java (assuming that you still have the Java JRE offline installer on your machine).
After having uninstalled both, make a search via START>Search>Files and Folders using the search query "limewire". Delete every found file except the installer.exe of LW. Then restart and install Java via JRE offline installer. Disable all sercurity software and then reboot again in Save Mode. While being in Save Mode install LW. Then restart again and look whether LW will open. If it does, enable all your security software again.

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