I'm in same boat. When I redid the house I'm in, I installed as much LED lighting as I could and the rest is halogen. What I've learned is, dimming range is based completely on the driver in the LED bulb. And most LED bulbs will only dim to about 20-30% of there maximum.
I'm sure you know how dimmers work, but for those that don't it is basically a super fast switch turning the light on and off very quickly. In incandescent bulbs, this works perfectly providing a nice smooth dimming range. In LED/CF's it is a nightmare for them to deal with. To get around it, they actually have to have extra circuitry to interpret the on/off pattern and then use that to control the brightness. During the on phase they pull extra power to provide power to the light during the off phase as well. For LED's, the driver reduces the voltage to the LED elements but never actually turns them off. So what normally would be dimmed to almost nothing for a incandescent, is pretty bright for an LED because it's pulling 2-3x as much wattage during that on phase to keep the capacitors charged and the light going.
TL;DR; For LED's, you have to look for high end bulbs that actually list their dimming range.
Now hopefully we will not be stuck for long with incandescent analog dimmers driving digital bulbs. There are a couple of standards trying to gain traction for pure digital dimming. These work by actually never dimming the power but instead sending a digital signal on the power line to tell the bulb to dim. Think philips hue bulb being controlled by a light switch instead of a wireless hub. But right now none are on the market for consumer level products.
There is a fight going on between your dimmer and your lights, and the dimmer lost.
One of the (too many) bits of electronics in your dimmer died.
Dimming is not as easy as it seems it should be, well, dimming without huge size, weight and heat.
In dimming led's, you are turning them on and off, fast, really fast, hundreds (or more) times a second fast.
For each of the on/off cycle, there are parts having to do work in the dimmer. Everytime electronics turn on, they make heat. Heat is the fastest way to kill electronics.
Your dimmer likely died in its really dim setting, and simply is not going to change.
Dimmer is gone - wants to be replaced
Best Answer
Virtually all new dimmer switches are "smart" switches. They contain tiny computer chips that control the dimming functions, and most smart switches have internal "parameters" that can be set with values to define things like minimum and maximum brightness, dimming speed, brightness step levels, etc. These switches often allow the user to change the parameters by holding the switch buttons down and tapping or clicking following a certain pattern.
For some reason I've found that certain people have a knack for messing up these switches - perhaps someone is holding down the dimmer button instead of clicking the paddle. It's incomprehensible to me how they manage to stumble into the pattern to mess up the parameters. And it's pretty much impossible to guess how to undo the damage without proper documentation. You'll need to read the manual for your specific switches to understand the different parameters and settings, and how to restore them.
You may find it easier to perform a "factory reset" on the switches, but be warned this could cause a home automation controller to forget the configuration for the switch. Then you'll find your lighting problems have suddenly become computer problems, and that's even less fun.
If they are part of a home automation system like Z-Wave or Iris, the parameters can be easily set and reset by the installer using the system controller and a computer.
As you read through the manual, look to see there is a parameter like "disable changing parameters from the switch". If so, I recommend setting it to avoid accidental repeats of this problem in the future.