I had issues with my firewall awhile back. Be sure to make an exception for the patcher/eq or, failing that, flat out turn it off while patching (make sure to turn it back on later -- Note: Many virus protection programs have their own firewall as well as many routers).
Make sure that your computer has it auto set to run as administrator, not just right click and hit run as administrator. (It sounds stupid, but they have 1000 people working on 1 operating system. Something is going to get lost in conversion)
As Huevos said, make sure the files are not going into program files. It has issues with this and the default folder is in program files. (Depending on how it's installed it would be C:/Programs Files/Everquest -- Or -- C:/Program Files/Sony/Everquest )