The carriage won't take me even when I'm naked, what do I need to do?
Solution 1:
Using a carriage: Talk to the guy, tell him where you want to go, walk to the backside of the carriage, look at the steps, and when the action-thingy pops up, activate it. Your character then will climb on by him/herself and gold is removed and the journey begins.
BUT: It is a fundamental rule in Skyrim that you cannot fast-travel if you are carrying to much weight.
Since travelling on a carriage "beams" you, after a loading screen, to your desired destination, it counts as fast-travelling. I love it that you got butt-naked ( :D ) but if you kept your armor in your inventory, you were still carrying the armor, thus carrying its weight. In order to be able to fast-travel (or use the carriage) you have to drop enough of the stuff in your inventory so you are no longer encumbered (I learned a new word, thank you! )
I have not tried it, but maybe drinking a potion of strength (increases your carrying-capacity for a certain amount, depending on the quality of the potion) and then using the carriage might help. But with the potion I'm just gessing. But if you drop enough weight, the carriage will take you where ever you want to go.
Solution 2:
An easy way to cheat the system is to get on a horse. Then it lets me fast travel I don't know why it just does.
Solution 3:
There is a console command that will allow you to adjust your maximum encumbrance weight.
Hit ~ to enter the console, then type the following and hit Enter:
player.modav carryweight 99999999
You can, of course, put whatever number you'd like in the final place. Be careful not to make it too big, or you may cause bugs.
Solution 4:
My solution was to hire him after you drop your things and are no longer carrying too much stuff.