My iMac G5 is not registering the connection of cable modem

Question

Something freaky happen to my computer one morning about a month ago and since then, I haven't been able to connect to the internet.
My computer is set to start up at a certain time in the a.m. and connects to the internet automatically. Recently, it started up before I awoke and when I did wake up I noticed that the my homepage for my web browser didn't load. I could tell moments later that there must have been a brief power outage to the home. I restarted my web browser and then the computer itself to no avail. I still could not connect to the internet.
I don't know a lot about computers from a technical standpoint, but I know a little. I looked at the network configurations to see if anything stood out. The one thing I noticed was the ethernet settings read to connect the ethernet cable to the computer. Since the cable was actually connected. I figured I may have a big problem on my hands.
The other issue I've noticed is the amount of time it takes to startup and shut down. It's not a very long time (maybe 5 minutes), but I think longer than normal or I remember prior to having internet issues.
If anyone has any clue to what may be going on with my machine, I would definitely appreciate some insight. All suggestion are welcomed.
BTW, I called a so called "Mac Specialist" in the town I reside in and was told that my computer's logic board needed to be replaced and it could cost me as much as $600. I most certainly hope that's not the only solution.
Thanks in advance!

Answer 1

There is a possibility the machine may have sustained some
damages due to a power surge, a brown-out or other variation
in electricity supplied to the machine from the grid.
An uninterruptible power supply with an automatic voltage
regulation circuit built into it is helpful to isolate computers
from the variations and unpredictability of some grid power.
This is not a surge protector. Those are not recommended.
You could try and see if repairing disk permissions in the
system by using that option in Disk Utility. Perhaps to
check and repair the hard disk drive, too, by using the
booted OS X installer's version of Disk Utility, is wise.
On the original OS installer packet disc #1 where the
Installer and Apple Hardware Test are located, it may
be wise, too, to run the Hardware Test to see if any
issues are reported or trouble indicated.
A reset of the power management unit or system manage-
ment controller, etc (whichever your model has) could be
helpful, even if it starts up and runs OK after an outage.
{And a re-install of the complete operating system on a
fully erased (wiped, overwritten with zeroes) reformatted
hard disk drive may be a part of this troubleshooting; if
you keep good records of what you do and how it was
done, even a fair tech should be able to tell you more
directly (if they are fair and honest) of the likelihood of
the hard disk drive being the cause of your problems.
-Doing this would destroy all of your stuff in the Mac.}
There is a chance that the hard disk drive may have a
few issues after a power incident, in some cases, a
few bad blocks or sections of the drive may be bad if
the machine's data was affected by an outage; these
can be checked and sometimes successfully repaired
by using a disk utility; some suggest use of DiskWarrior.
Have you been able to test the cable modem itself;
perhaps reset the modem and then reattach the
computer to it; or see if it works with another computer?
Sometimes, even booting the computer in SafeBoot mode
and then login, then choose to run Disk Utility's repair disk
permissions, and then restart the computer normally, helps.
Have you tried a second user account to see if the issue
of connectivity is isolated to the main or admin account?
Usually, all accounts share the main connection settings.
Sometimes, checking and re-affirming settings can help;
at least as part of a troubleshooting path, to see what
doesn't fix it, and hope to find something which does.
If the issue does come down to a hardware repair of
more than a reasonable percentage of a refurbished
Mac direct from the Apple Store online, consider a
different computer. Even the low-end Intel based iMac
is leaps ahead of the G5 iMac. (I still have G4s!)
PS: What are you using to get online?
In any event...
Good luck & happy computing!