Doorbell became very soft, battery replacement only necessary?
Seeing screws with wires attached to them is a good sign the doorbell is hardwired (not battery operated), in a battery operated fixture the wires would be soldered to a circuit board.

If you live in the U.S. you are probably dealing with 12 to 24v at the chime, though the power should still be shut off at the main panel before you start working.

Here is a good guide to troubleshooting a doorbell.


  Troubleshoot a doorbell switch
  
  
  Unscrew the switch from the house and pull it away to tighten any loose
  wires.
  If that fails, bypass the switch by shorting across the terminals with
  a screwdriver blade or by removing the
  two wires and touching them together.
  If the bell rings, replace the switch.
  If not, twist the two wires together
  and move on to the next step.
  Connect the two wires to the two terminals; push the wires back into
  the wall and screw on the switch. If
  new mounting holes are required, start
  the holes with an awl and drive in the
  screws.
  
  
  Troubleshoot a transformer
  
  
  Locate the transformer, and inspect and tighten low-voltage wire
  connections to it.
  If neither doorbell works, use a multitester set to the 50-volt AC
  range to test the transformer. Touch
  the probes to the two terminals. If
  the reading is within 2 volts of the
  transformer's rating, troubleshoot the
  chime. If not, go on to the next step.
  Shut off the power to the transformer's circuit at the service
  panel, and remove the outlet-box
  cover. To test for power, pull out the
  black circuit wire and remove the wire
  nut. Probe the black and grounding
  wires with a neon tester. Repeat the
  test for white and grounding wires.
  Tighten any loose connections.
  To replace a faulty transformer, remove the low-voltage wires. When
  there is more than one wire at a
  terminal, tape them together for
  easier rewiring.
  Shut off the power to the doorbell circuit at the main service panel.
  Remove the outlet-box cover and
  disconnect the wires from the old
  transformer, then disconnect it from
  the box or the box's cover.
  Attach and wire the replacement. Connect the transformer's green wire
  to the bare grounded wire and its
  other two wires to the black and white
  circuit wires. Attach the outlet-box
  cover and secure each low-voltage wire
  or set of wires under a terminal.
  
  
  Troubleshoot a chime
  
  
  Remove the chime cover, which may snap or screw onto the base, and
  inspect all wiring connections.
  If the connections look good, set a multitester to the 50-volt AC range,
  then touch one probe to the
  transformer terminal and the other to
  the nonworking front or rear terminal.
  If it fails the test, replace the
  faulty wiring (see "Replace doorbell
  wiring," below). If the chime has
  power but neither doorbell works,
  replace the chime (go on to steps 3
  and 4).
  To replace a chime, remove its cover. Disconnect and label the wires
  for easier rewiring. Remove the
  mounting screws and the old chime.
  Thread the wires into the back of the new chime and mount it to the wall
  with the provided screws and anchors.
  Attach low-voltage wires to their
  respective terminals and replace the
  cover.
  
  
  Replace doorbell wiring
  
  
  Disconnect the faulty wire at both ends and loosen or remove all
  accessible wire staples.
  Twist together one end of the existing wire to an end of the new
  wiring and tape the splice, using very
  little tape. Pull the existing wire to
  draw the new wire through holes,
  staples and wall or ceiling cavities.
  Pull it through one section at a time
  rather than all at once. Staple as
  needed.