Issue with powering an MRK 1000 with a li-po battery

Hello! I am working on a project where I am using an Arduino MKR 1000 to input distance measurements from a MaxSonar LV ultrasonic range finder, and output auditory feedback through a headphone jack. My soldered setup can be seen in the photo below. My device works perfectly fine while connected to USB power, however my goal is to have it powered by a small li-po battery that connects to the battery input on the bottom right corner of the Arduino (see picture). I have tried different types of batteries; the first two were 230 mAh (3.8V) and 150 mAh (3.7V), and these would not turn the Arduino on. The next battery I tried was 800 mAh (3.7V), which worked while the Arduino was also connected to USB power, however when I disconnected USB power the Arduino read ‘zero’ or ‘null’ measurements. The last batteries I tried were 1200 mAh and 1500 mAh (3.7V) batteries, where as soon as I plugged them in, the board started smoking.

I am trying to find a battery that is compatible for use with the Arduino MKR 1000. If anyone could tell me what type of li-po battery I can use, that would be greatly appreciated!

Also an aside, I am trying not to use a portable battery pack as USB power, because the battery pack shuts off after 30 seconds. I believe this has to do with the voltage regulator on the battery detecting very little current being drawn by the Arduino, so the battery automatically turns off. If anyone knows how to solve this issue, or knows any portable USB battery that works with an Arduino MKR 1000, that would be greatly appreciated!

The mAh capacity of a battery has no direct effect on its voltage.

That you are seeing differences suggests that you may be be drawing excess current from the batteries.

In particular that the board is 'smoking' when one battery is connected is a strong indication of something very wrong.

So what is the current your board is drawing from the batteries ?

What I have discovered is that the polarity of the battery connector is not universal. On the MKR1000 board the positive terminal of the connector is on the side nearest the USB socket on the board:

In your screenshots, the first battery's connector has the correct polarity, but the other three do not:

I had the same problem with the JST PH pigtails I bought. What you can do is use something sharp like a safety pin or push pin to pry up the plastic locking tab (indicated by the red circle and arrow on the image below) on the connector just enough so that it no longer locks in the metal insert, then pull the wire and metal insert out of the connector housing. Do that with both wires, then push the inserts back into the housing in the arrangement that matches the MKR1000's connector polarity.

As for the smoke, when that happens it usually means you'll need to buy a new Arduino board.