ILI9341 LCD Possibly Damaged

I tried connecting a ILI9341 LCD to the espruino, however almost immediately after connecting VCC and GND (to BAT and GND respectively) and giving it power, a small component on the back began smoking. While I disconnected it as quickly as possible, I'm not sure if this damaged the LCD.

I tried connecting it to a 3.3V pin instead, which did not cause the component to begin smoking, but seems to short out the board in some way, as it stops responding to input and cannot be connected to the computer until the VCC wire is removed. I also noticed that LED1 on the espruino glows faintly when VCC and GND for the LCD are connected.

Any idea what the issue is? I made sure I didn't have the wires backwards. If I run the code in the Code Examples section for the LCD without VCC plugged in, the screen lights up white, so it seems to be at least semi-functional.

Check and recheck your connections at both ends...
Barring wiring issues, it sounds to me like there's a short on the board between VCC and GND - with VBat, enough current was able to flow to make it smoke, whereas on 3.3, it's limited by the Espruino's 3.3v regulator, and ends up pulling the voltage below 3.3v, resulting in the espruino resetting.

Most of the modules I see on ebay advertise that they'll work on 5v input, so it should have worked on 5v...

As for why the screen lit up when you ran the sample, that's just because the LED pin drive the LED backlighting on the display. This doesn't go through the controller.

I looked up information on the board from the manufacturer and it says the input voltage can only go as high as 3.3V. Darnit ebay...

I'm pretty sure that you're right about it being a short. I've rechecked my wiring several times and it seems like that's not the problem. Time to give up and try another LCD? I doubt I could do much to fix it (or that it would be worth the time and effort for a $5 display).

I guess it's best to try another - it might be worth just looking over the LCD board and seeing if there are any solder splashes on it or misaligned components? They're most likely to be the things causing a short.... The actual controller chip is on the LCD itself (not the PCB) so it's probably fine (unless that was the thing that was smoking!).