My wife got a Moleskin Booklight for herself and it didn't work right. It only worked when it was plugged in to a USB port, never on battery power. I'm not the first one to have this problem, and 1o_o7 did a nice instructable on it here.
The nut of the problem seem to be that the battery isn't charging. This can be fixed by wiring to he USB power rails directly to the battery, but then you are bypassing the battery protection. I did a little poking around, and found that the battery started charging when the ground pin of one of the IC's was lifted. My suspicion is that the IC was installed backwards, but unfortunately I broke the bent pin while removing it, so I couldn't prove it.
Anyway, I decided to replace the IC. After doing so, the battery started charging and the light started working, so I think I can say that for my particular light, the problem was the battery protection IC, which was either defective or improperly installed.
I could not find the actual IC they used at regular retail electronics sites, so I picked out a substitute. I should sat that I chose it based on matching footprint, the matching pinout, and the fact that it was available. According to the datasheet, this IC comes in 40-odd flavors with different over-voltage and over-current detection levels, so it's unlikely that it matches the original exactly. I make no promises or warranties, and your circuit repair is at your own risk- I probably wouldn't leave it to charge unsupervised overnight.
Before I go in to the actual instructable, I would like to point out that after I did this, I did NOT test the battery protection.There is still a risk of overcharging (which can lead to over-heating and possibly over-flaming) and deep discharging (which will reduce the battery life). Mine hasn't caught fire yet, but I've only had it working a day or so. That said, the charging light goes on and off when it is supposed to now, so there's that.
The first step in my instructable is to take the thing apart, as per 1o_o7's instructable, so you will need everything you need for that. In addition, you will need a replacement for the IC, similar to this.
Step 1: Remove the Old IC
Disconnect the power and remove the battery protection IC. If you have rework tweezers, this is pretty straightforward. If not, my suggestion is to melt a big glob of solder across three pins on one side. Then heat the glob until all three pins begin to loosen, and gently pry them up. Repeat for the other side. If you have to, go back and forth until both sides are free.
If you want to try and reinstall the same IC (to see if it was backwards), you will have to remove it in one piece, which is better than I could do.
Clean the pads up. Again, my procedure is to melt some blobs of extra solder on the old solder to heat it and make it flow, then go over it with a solder wick. If you are feeling ambitious, a little isopropyl alcohol and a q-tip will make it look tidy.
Step 2: Install the New IC
Put a little dab of solder on one of the pads, then hold the iron on it to keep it hot while you position the IC over the pads. Remember to position it as in the picture- the "top"goes to the right, away from the other IC. The top should be marked with a line across the top or a dot in the upper left corner. When you have it in place, remove the iron and the solder will hold the IC in place while you dab the other five pins.
This can be a little tricky if you've never done surface mount IC's, especially as there didn't seem to be any solder mask between the pads. When I did mine it was really easy to bridge between the pins. If you have a solder bridge between two pins, they will be connected electrically and the circuit will not work as planned. Be careful, and use little tiny dabs of solder to start with.
Step 3: Power Up the Board
Gingerly apply power to the two tabs at the bottom of the board. I used an external power supply, but you could take it from the USB plug too.
I like to feel the battery for a while while it's charging. It shouldn't get hot- nothing on the board should get hot. The charging light will come on while the power is plugged in
Step 4: Try the Light
After letting the battery charge for a few minutes, disconnect the power and try the button. The two white LEDs should toggle on and off. Success!
Step 5: Charge the Battery
You are now ready to fully charge the battery. Like I mentioned at the beginning, I did not do any deep testing on this. The reason there is a battery protection IC in the charging circuit is because it needs to be there in order to sell the product- whatever offshore contract firm did this did not add 36 cents to the bill of materials for your piece of mind.
My advice would be to watch it charge, at least a couple of times. Charge it at your desk while you are working on something else. If you smell smoke, unplug it. Don't leave it lighting or charging by itself. This is probably overcautious of me, but I would feel bad if you got burned by my instructable ; )