Engine will not crank over? Starter is not working?

Iv'e noticed that my car has problems starting mostly during the winter time. Usually I have to let it sit for a little while and it will start again. Recently Ive noticed that its getting worse and now takes an hour or so to resetstart. I checked the battery, and alternator, and they are good. Also my dash lights and knobs go up and down and on and off like the car is posessed from time to time. The dealer says they will have to keep my car for 2-3 days to go over everything because it sounds like an electrical problem. Some say its the starter, and others say it has something to do with my remote start not working. Please help!