Did you TEST the NEW battery???
Clean the battery contacts points (with the puter unplugged)
with a Q-tip soaked with a couple drops of 70% rubbing alcohol.
Let it dry for a couple of hours before plugging it back in and
re-booting so you don't short out the board.
Upon re-booting, set the time and date and shut it down overnight.
If the time reads correctly in the morning, problem solved.
If it's still acting up, have the BIOS chip checked for an update.