Memory of old battery?

I bought a new battery for my Nexus7 (2012 Wifi) and successfully replaced with it. However, length of time that I can operate is only 3 to 4 hours, which is the same as the old battery before replacement.

I claimed the seller about it and a new battery is supplied from the seller. But the next one also allowed operation of only 3 hours. According to seller, it may be due to the Nexus7 remember the output pattern of the old battery.

There is another problem. After the replacement, my Nexus7 cannot be charged while it is turned off. It is very strange because when I plugged the cable, the animated sign of charging is displayed. Even after connecting the cable for several hours, the remaining battery is unchanged. If the Nexus7 is turned on and sleeping, it can be charged.

Do you think this strange phenomenon and the short operating time are really due to the memory of the old battery?