Nick,
I would first try this procedure:
http://docs.info.apple.com/article.html?artnum=58462
You may also be correct regarding a failed solder joint at the power port. This is a quote from an Apple moderator some time ago.
------------quote------------
This sounds like a classic symptom from the PowerBook 5300/190 REA
Program. It is caused by the AC adapter port breaking loose from the
logic board and cuasing intermittent connections. When you don't realze
this is happening it will drain your battery and then shut down. It
usually confuses the power manager in the bargain. The clicking sound or
green light may also appear. You need to pull the battery and AC adapter
and hold the reset button in, sometimes a few times until the clicking
from the speaker goes away. Then leave the battery out and put the AC
adapter in. With gentle side pressure (you will have to experiment which
direction) on the AC adapter plug at the back of the PowerBook, try to
start it up. You may be successful, and able to do some work before you
send it in for repair. (I have one running with a rubberband to give it
the side pressure, until I get around to sending it in) If you are not
successful in starting it up, there is nothing o do in the interim. You
need to get hold of an Apple-authorized service provider and have this
serviced under the program.
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