See photo. Is this a normal LED? I'm trying to troubleshoot it and can't tell if the bulb\diode is fine.
It's an LED.
Easiest way to see if it is damaged is to connect it to a battery and see if it lights up.
The difficulty is that you can't disassemble the the white plastic unit, so if the LED does not light, the connection wires, resistor or LED itself may be damaged.
If you have a voltmeter you could measure the resistance across the terminals. It should be infinite one way, tens of ohms the other. If it's infinite both ways or zero either way it's trash.
Good news is that decent quality rechargeable LED lights are now inexpensive and ubiquitous.
There's a circuit board inside the white plastic bit, which is called an LED driver.
Here's an example http://www.dx.com/p/3-6v-16v-925ma-constant-current-led-driver-board-for-cree-and-ssc-leds-4pcs-506226#.W26FJ3b-hhE which looks like this:
The red and black leads go to the LED and the two round metal tracks on the other side are for interfacing to supply battery. The specs relate to voltage out, and supply voltage available as well as maximum currents.
Given your light is not working now, you're not going to make it worse with some exploratory surgery.
Now some observations:
There is no thermal conductor around that unit. Its all plastic. Normally a high-power LED makes a lot of heat that must be removed by passive heatsinks.
So if your light isn't obviously damaged on inspection (loose wire or leaked battery or corrosion) then its probably best to junk the light and buy something newer. Its done its service, time to retire it.