Can't send HTTP POST when only connected with battery

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.

Am I supposed to be able to use the GSM module with only the battery?
Is the "on" LED supposed to be enabled when only the battery is connected?

Hi,
On led is not supposed turn on when battery operated as this allows saving some current. I suppose you're on a 2g network in which case you should modify the board shorting the PTC resettable fuse on the board in series with the battery which is limiting the current the battery can provide.