Welcome, Joe!
What you experienced is called a "kernel panic" (or "KP") and you can read up on them here:
http://thexlab.com/faqs/kernelpanics.html
There is a huge gap between "nothing wrong" and "replace the logic board" when it comes to KPs, so don't call the undertaker just yet.
1) Many KPs are caused by defective or incompatible RAM. Although rare, a RAM module can fail from age and heat. Have you added RAM lately? If so, remove the most recently added module and test either without it or with the old one reinstalled.
2) A fault in an attached peripheral can sometimes trigger a KP. Test with no external devices (printers, external hard drives, etc.) attached.
3) KPs can be due to a software incompatibility. Have you added any new software recently? That includes programs like drivers that support hardware device
4) As you have never upgraded your OS (you can get to 10.4.11 without cost) there could be an outdated software component in your system that has decided it's had enough. 10.4.11 is very nice--you should try it.
Mac OSX tracks various crashes and failures via a system of logs written to the HD. Your KP will be detailed in a file called
panic.log. Whether we mere mortals can
fully understand them is a topic of discussion, but we can try.
In
Applications > Utilities, find and Launch the utility
Console. When it opens, click the "Logs" icon and the left end of the windows menubar. This opens a navigation pane to help you meander through the various file types. Note that several entries in the nav pane have those little gray disclosure arrows. Click the one next to
/Library/Logs.
NOTE: this is NOT the similar-looking one that starts with a tilde (~).
Toward the bottom of the freshly displayed list should be "panic.log" Select it and you should see some gibberish in the main pane. Scroll to find the part of the log that matches the date of your KP. Copy/paste it here, first making sure the info does not contain any computer serial numbers.
If the KP is hardware related, the log may not help as the hardware fault info was coded by a drunken Klingon. However, if software related, I can often see enough to come up with an action plan.
Sorry this grew long but I didn't want you to toss the computer just yet, as most KPs can be resolved without spending big bux.