Welcome to our little internet campfire.
Your internet settings may be set to disconnect you if you've been idle for a time. Go to:
System Preferences -> Network -> PPPoE tab
If you are connecting via the internal modem, there will be no
PPPoE tab. Instead, there will be a
PPP tab, use it instead.
Click the button near the bottom of the pane that says
PPPoE Options... (or says
PPP Options... if you are connected via modem).
A sheet will slide down with various options. There is a checkbox to disconnect if idle for xxx minutes. Uncheck the box if it's checked. Also uncheck the box to prompt every xxx minutes to maintain connection. Those options were probably implemented for years ago, when ISPs charged by connection time. It's also useful on a Windows box, to limit exposure to the internet. On a Mac, those two options are just annoying to the user.
If you changed any checkboxes, click the
OK button and the options sheet will slide back up. Now click the
Apply Now button at the bottom of the main pref pane and the revised settings will be set.
The crashing may come from disk damage, caused by improper shutdowns. Boot from your OSX Install CD. When it gets to the Installer, go up to the menu bar. Under the File menu (or the Apple menu, I don't remember which exactly), there is a choice to go to Disk Utility. Choose it. The Installer will quit and Disk Utility will open. Select your hard drive, and do a Repair on it. Assuming the utility is able to repair is, then do a Permissions repair for good measure.
If no problems are found (or the problem persists), boot from your Apple Hardware Diagnostics disk and run the tests, see if there is a hardware problem.
If there is substantial disk damage, Disk Utility may advise you that it cannot repair the damage. In that case, you need to either:
1) get DiskWarrior or TechTool Pro and let them fix it.
or 2) backup, reformat the hard drive, and reinstall.
Option #1 is generally preferred over option #2.
Crashing can be caused by a number of things. The steps outlined above are a good place to start, and generally free. If they don't fix the problem, let us know what happened when you tried them. We'll suggest additional steps based on what you find out.
Oh, it may be helpful if you told us what model you have, the OS version, and your various hardware specs. We know it's a G5, and that you have broadband, which suggests an external modem - possibly connected via ethernet. We don't know if you've added RAM, what video card is in use, or even your OS version. What PCI cards are present, what's plugged into the USB and FireWire ports. If AirPort is installed, or if you are booting from a RAID array connected via fibrechannel card. All of this could be important - for example, if you are running Tiger (OSX 10.4), DiskWarrior isn't compatible ... yet. An update is expected any day now.
Do the lights flicker where your G5 is? Dirty power lines can cause crashes too. We need a bit more info.
Oh, and don't bother with Norton antivirus. We don't have any virus problems today.