Before tearing into the computer, let's do some probing that may allow less intrusive intervention. It's possible to trash a PowerBook with one little slip-up during take-apart.
the computer runs for about a minute or two then goes to sleep.
Does this happen on battery, A/C power, or both?
If on battery, neither charge level or heath may tell the whole story. My PBG4 was 5 years old when given to me with the original battery. The battery had only 100 cycles in five years (too few) but displayed decent retained charge and runtime. However, it would only run so long on battery and shut down abruptly at the same charge level of about 60 percent. An Apple tech looked at it and said the batteries have several cells within. Should one go bad, the computer will shut down within a percent or two of the same charge level every time. The only cure is a new battery.
If it does this on wall power as well, it could be overheating due to a runaway background process or a bad fan or fan sensor. The computer has thermal protection that shuts it down if temps become dangerous. If a fan sensor goes bad, the fans are set to switch to full-speed mode to prevent overheating. If the fan motor goes, you get no warning unless you have temperature-monitoring software installed.
This Dashborad widget:
http://www.apple.com/downloads/dashboard/status/istatpro.html
defects both temperature and fan speed. If a fan is not showing about 2000+ rpm, you have a dead fan. If a fans shows it's dong about 6000 rpm, there is a dead temp sensor somewhere.