I've been working with the MKR GSM 1400, works just fine as long as I'm connected via USB with no battery.
If I connect the battery (3.7v LIPO 2000mAh - also tried 1200mAh) and disconnect the USB, the GSM doesn't make the HTTP POST. The board heats up and stops about as frequently as I attempt the HTTP POST, without success. The "ON" LED doesn't turn on, also the "L" LED at the end of the pins doesn't turn on either.
If I put both the battery and the USB, the board heats up and the "L" LED dims very low while the "ON" LED stays on, the HTTP POST fails.
I did disable all Serial communication code when I connect the battery and disconnect the USB.
I'm reading that many are having problem with this board, but the issues I'm facing seem different.