Battery charger specs and operation

Ladies and Gentlemen,

I call upon your expertise to help me find a detailed explanation of the different states for the charging system and indicator LED. I recently purchased a larger battery having read somewhere that the real problem with these units is putting too small a battery on them. So when I plugged in the PKCELL LP803860 2000mAh 3.7V battery pack the unit initially powered up with 3.7VDC available from the battery. When I plugged in the USB cable from my computer I was alarmed to see the run light go to a very dim state and the charge light was illuminated very dimly also. The system voltage was only around 1.3VDC and I theorized (possibly wrongly) that the capacity of the new battery called for extra current because it may not have been fully charged when it arrived at my home. I left it overnight and by morning the run light was fully illuminated and the MKR1400 was communicating with my computer. The Charge LED was flashing at a rate of once per second. I unplugged the USB cable and noted the battery no longer would power the board. For all intents an purposes the new battery is now non-functional. The actual battery voltage is now 3.4VDC. I replaced the battery with my original PKCELL LP503652 1200mAh 3.7V one and the board seems to function properly but after about 24hours of run time plugged into the computer I now see the Charge LED flashes briefly once every 3-15 seconds.

Clearly there is a basic understanding of charger operation I am not understanding. Please help me find the write-up of charger operation and Arduino's recommendations for battery capacity.

Mike