The level of disassembly required to replace a 1/2AA 3.6v lithium battery
on the logic board of this type of computer is not something an average
user would be equipped to complete; or if they did, without the proper
knowledge, skill, any special tools or supplies, there may be issues or
damage to the computer.
The take-down process is published online at a few web sites, on how
to open the computer, steps to take, what you'd need, including the
fact the bottom inner layer of computer requires re-torquing when it
is reassembled; thermal paste and a torx-type of screwdriver, a new
battery, and careful handling of the parts inside is required. Anything
short of near perfection, and damage to other parts inside may result.
iMac G4 Take-apart for drive and ram upgrades:
http://www.xlr8yourmac.com/systems/imacg4/imacg4takeapart.html
http://www.faqintosh.com/risorse/en/guides/hw/imac/g417hd/
{The battery access level is on the main board, where hard drive and
other major components are also accessible by an expert.}
So, since that area of the computer was not intended to be user-accessed,
the information you read about it confirms the (esp under warranty) need
to have someone trained and able to perform the procedure for end users.
Replacing the battery on the logic board would require a minimum shop time
and in some cases, a technician may be able to test the hardware and do
the battery replacement. Of course, there is a chance the power supply has
failed; but a tech could use a multi-meter and test the computer without
taking it apart, since there are test ports beneath the bottom cover near the
PMU reset button, airport card slot, and SO-DIMM ram slot.
There are some shops out there who will still work on these iMac models;
you may have to ask if there are other independent specialists near you.
Even smaller cities have a few, and others may have no trouble testing it.
Good luck & happy computing! 🙂