Step ONE! Stop trying to work the devices live. Even experienced electricians do not do that unless it is absolutely unavoidable! Remove the fuse or turn off the circuit breaker that powers that circuit before doing any more work.
If there is anyone else present that you aren't "lead pipe" sure would never mess with the circuit's fuse or breaker then remove it and remove any spares that they might use to replace it and take those with you until you are ready to re-energize the circuit. This is seldom an issue in single family homes but it is a problem in multi-dwelling buildings were the panel is not within the unit it serves.
By the burn marks on the brass terminal with the red wire on it I would guess that you caught the edge of the adjacent dimmer switch when you were pulling the the cover plate of the box. When the device; in your case the double stack switch; will not sit firmly on the box face and still fit tightly in the face plate then the installer may have used the face plate to hold the double stack switch in place. You remove the face plate and the double stack switch moves so that its terminal touches the heat sink fin of the adjacent dimmer. PIFT the circuit shorts to ground and the Over Current Protective Device (OCPD); fuse or circuit breaker; opens the circuit and clears the fault before arcing can generate enough heat to do more damage or kindle a fire.
BE AWARE THAT THE OCPD WILL PASS MORE THAN ENOUGH CURRENT TO TAKE YOUR LIFE; that only takes 30 milliamperes which is only 3 hundredths of an ampere; prior to opening the circuit. STOP WORKING ELECTRICAL CIRCUITS WHILE THEY ARE STILL ENERGIZED. Am I repeating myself? Why yes I am. In addition to having worked as an electrician for almost 50 years I also served as a Firefighter/ Rescuer (EMT) for 45 years. I have run many calls for electric shock and more than 1 of them had resulted in Electrocution. In 2 cases we had to wait for the Coroner's staff while surrounded by a greiving family. That does tend to make one a little touchy on the issue of live work!
Check that the terminal screws on the double switch are tight but use only your wrist and not your forearm when checking. You need to avoid stripping the threads out of the the plates into which the screws are mounted. Wrap the whole switch in 3 layers of electrical tape under the mounting screws. Remove the mounting screws before taping. Calculate the watts of lighting that are controlled by the dimmer switch and if it is less than half the maximum capacity that is marked on the face of the dimmer then you can break off the fins on that side to give yourself room to safely reinstall the double stack switch. If you want the extra protection against faulting it again then buy an
plastic electrical box extender.
Install the box extender right up against the front of the box because in this case it is serving as an insulated divider between the two devices and not to actually extend the box. You will have to install that right against the edge of the adjacent dimmer switch and it will be a challenge to make it fit. If the mounting screws still aren't tight enough to hold the double stack switch still then by a box spacer of the appropriate thickness and mount it behind the mounting ears of the box extender so that when the double stack switch is installed it will be held tightly in place.
Now you can actually try to find the open connection which stopped the ceiling fan from working. The bad news is that many ceiling fans are not well designed so as to facilitate checking the connections with the ceiling fan still mounted. If you remove the ceiling fan you will have opened the splices which are the most likely culprits to have failed because of the vibration caused by the fan they supply.
If you have any more questions please ask. Oh and one last thing. DON' WORK THE CIRCUIT HOT!
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Tom Horne