tech4all said:
I haven't got any kernal panics, although I did that notice that said I needed to restart my computer by pressing the power button for 10 seconds (or something like that).
Actually, that message is Apple's polite way of informing you of a kernel panic (which is another word for the OS crashing).
You describe at least three complete OS crashes over a period of a few days, which is a surefire sign that something is very much not right with the system; I run my G5 tower for weeks without problems like that.
You have no external hardware (that would cause issues) connected, so that's easy to rule out, leaving either a piece of software that modifies the system itself (Virex is the only possible culprit you mentioned, though I wasn't aware it caused that many problems), but things like Norton SystemWorks may also install things that can cause instability. Run of the mill programs, however, cannot.
The other possibilities are a bad OS install, which you'd diagnose by reinstalling the OS and all updates, or a hardware issue, either with your drive (which sounds quite possible), or with another component in the G5. It'd be worth taking the metal panel off the side the next time it's making that whirring sound and seeing if the noise is definitely coming from the hard drive by putting your ear near it.
tech4all said:
when I first turn on the computer my internet connection is screwy, like Mail won't connect to my email servers and I may have trouble getting to my homepage in my browser (Safari). However, if I reboot the computer after first start up, it goes online quick, and Mail works wonderfully
This sounds like a symptom of a flaky internet connection; less likely a problem with the computer itself. If you're using DSL and the service uses PPPoE, it might be taking a while to connect, particularly if you're using a router or AirPort in between. I've noticed that inputting your DNS servers into the Network Preference Pane manually in this case fixes the issue, though there's probably a better workaround.
To confirm that it's not your computer, try this: Turn the machine on, try to connect to the internet. Assuming it doesn't work the first time, open the Network preferences, select your ethernet connection, then in the TCP/IP tab click "Renew DHCP Lease"; if it works after that, it's probably your slow-responding DSL modem or router.
tech4all said:
Oh btw: the hardware test CD thing is on the CD(s) that came with the computer right? Yea I know I could check, but I have to go somewhere right now

And when get that CD in the computer, how do do the hardware test thing? What will tell me? Thanks again!
It'll either be on a seperate disc or included with the "restore" disc. If it's on its own disc (probably not), just put it in and hold the "C" key when you restart. If it's on the restore disc, there should be instructions for using it printed on the disc itself (the manual will also tell you, I assume).
Since you have Applecare, you might just call them and ask them for help, since it's free and they'll be able to listen to what you're hearing if you can get it to happen when they're on the phone.