I would like to add a dimmer to a circuit of lights controlled by 3 switches. Will three-way dimmer work, and if so, in any particular location? Thanks

My wife thought her hair dryer was broken because it would not work in any of the four plugs in the bathroom. One is a GFCI outlet that is feeding a second outlet on the other side of the mirror. She bought a new hair dryer and it did not work either. I checked and the GFCI outlet was not tripped. I tripped it and reset it but the outlet still did not work. I went to the basement and found the 20 amp breaker that serviced the bathroom outlets and tripped and reset the outlet. She was able to start drying her hair but it went out again. I dug out a volt meter and I could get 120v from hot to ground but only about 45v from hot to neutral. I pulled the cover off the electrical panel and found: [URL=http://www.kevinandjudy.com/badwire.jpg]picture of inside of breaker box[/URL] The screw is tight. I am guessing the wire is loose. I am a little afraid to go poking around in the box with the power on. Why would they cram bundles of neutrals into one screw terminal when there are 15 or so empty ones below? To fix this can I remove the chared wire, cut it back to where it looks fine, pigtail on an extension and run it to its own screw terminal? There is no sign of arcing at the receptical end. The only thing on the circuit is the two bath room recepticals. The wire appears to be 12 gauge wire. The house is 7 years old and all the wiring and breakers are original. Am I right that the only cause would be a loose neutral wire at the bus bar?