The 'charger port' is where the DC-in Board is located, behind that port.
To fix the port implies replacement of the port on small circuit behind it.
Does the power adapter DC plug have an illuminated end that changes
color from yellow to green, etc? If that has it, and that is working it does
indicate power; however do not expect the dead battery to charge up.
http://eshop.macsales.com/shop/apple_laptop/batteries/PowerBook_G4_15_Ti
http://eshop.macsales.com/shop/powerbook-ibook-macbook/
The computer may start without the battery in, if it could start up at all.
Some users leave the battery in there, and then let the computer set
and try to charge for maybe 10 hours. This is to see if there can be
enough power stored to get around the failed backup or clock battery.
(To try the PRAM reset, according to instruction, may help. Could be
the original hard disk drive may also be shot. It could be froze up.)
After doing some backward research, your PowerBook G4 model is the
first build-model G4 series PowerBook. It also has a pram/clock battery
on the logic board, that if dead, may disallow the computer from startup
even if the main power cell is good and has a charge. The old battery is
very unlikely to sustain any viable charge capability after so many years.
PowerBook G4 info - http://mactracker.ca free database download spec
{The part number for the backup battery is 922-4361 -- this is a tiny cell
on the logic board, and requires a tedious take-apart to access it... and
it may be possible to disconnect this battery, to get the PB to start.}
The system software you have hopefully is the correct original disc set
since they are hard or almost impossible to buy, they are series specific.
You could get and run as new as Tiger OS X 10.4.11, w/ 1024MB RAM.
Original OS | Mac OS 9.1 |
Later OS | Mac OS 9.1 and Mac OS X 10.1.1 (5M45) |
Maximum OS | Mac OS X 10.4.11 |
Hardware Test | AHT (PowerBook) 1.1, 1.2, 1.2.1, 1.2.2, 1.2.3 |
Maximum Memory | 1.0 GB |
Memory Slots | 2 - PC-100 3.3V 144-pin SO-DIMM |
System Battery | 50 Wh Lithium Ion (M8244G/A) |
Battery Life | Up to 5 hours |
Backup Battery | 922-4361 |
Power Adapter | PB G4 Power Adapter (M8243**/A) |
{specs cited from http://mactracker.ca database}
Original system discs usually include an Apple Hardware Test.
So that should be among the artifacts you have with it.
You may have to look around for a backup clock battery
and someone to install it; there are online sources for
parts, such as powerbookmedic, wegenermedia, OWC.
The computer is old enough to hope some Apple Specialist
or independent repairer with experience in older Macs is
within your area, or consider mailing it away to one.
Part of the process now, to troubleshoot why it won't work
invites various partial repair & parts replacement to test it.
Perhaps that may end up also needing a new hard drive.
If so, that requires an Ultra ATA/66 (ATA-5) compatible HD.
•PowerBook G4 Titanium (Mercury) Repair Guide: iFixit.com
http://www.ifixit.com/Device/PowerBook_G4_Titanium_Mercury
Information on parts, placement, and access are in the guide.
However these are tedious and unskilled unfamilar efforts to
attempt a repair could cause additional damages & so as to
make the original issue(s) harder to diagnose & further repair.
Not sure how much any of this helps...
Good luck & happy computing! 🙂