With an SMC reset the battery reporting may be more accurate; though had
you tried this quite some time ago the issue may have been delayed, but as
the battery is now even more worn out, a replacement should be purchased.
•How to identify Mac Pro models - Apple Support
Note there are different instructions for use of the SMC reset depending on
which version of portable Mac you have (also desktop model) so be sure in
regard to SMC reset, the correct instruction for a Portable depends on if the
one you have, has a battery that you could replace yourself, or one that is
considered to not be user-replaceable.
•Resetting the System Management Controller (SMC) on your Mac - Apple Support
But the very real likelihood is that battery is beyond help, while the reset may
only serve to report its status more accurately. The system hardware profile
can show you the total number of battery cycles, and that's an indicator, too.
•Mac notebooks: All about batteries - Apple Support
•Apple Portables: Troubleshooting MagSafe adapters - Apple Support
Another item to have checked, once the battery is replaced (or by the tech who
may replace a built-in battery, if your MacBook Pro is a newer model) is the
status of the MacSafe DC-in Board to see if that part is functioning correctly.
Good luck & happy computing! 🙂