What would happen if I plugged in too many internal HDDs into my computer? If my PSU is only 450W, and it didn't have enough juice to power them all, what would happen when I turn the power on?

It would depend upon the power supply. Power supplies are not born equal. :-) If it was a serious overload, hopefully it would trip the circuit breaker/overload protector. That's the way it's supposed to work. However, hard drives do not draw very much current (maybe 15W) and you would really need a bunch to cause a problem. The heavy loads are the newer CPU and graphic cards.

I have a fanless (read: MASSIVE heatsink) PSU, and 8HDD's (P4 3.2, 2GB DDR, old MOBO, Geoforce FX 5600). Putting that into the typical online PSU calculator tells me I need a 630W PSU. Problem: my PSU is rated 450W. Yes, my PC recently died, and after testing/removing all non-essentials (all HDDs, IDE cards, replaced RAM/Video card, running OS from CD Drive, etc), I figure the ancient old CPU or MOBO has died... with no way to swap test.. but now a friend mentions the online calculator, and it turns out my PSU has been overloaded for years. With my old set, 3 HDDs were the maximum before going over 450W. I've had at least 6 HDD's in for years, with two more added over 6 month ago. And yet the glitches, then crashes, then showing nothing on the monitor (fans spin, HDDs spin) all happened in the last two weeks. Weird.

You can't judge a PSU solely on wattage. And wattage calculators aren't very useful because they don't calculate amperage. Check the amperage rating for the +12v rail on your PSU, then do the math & see if you've been overloading it: P4 = approx 10A each HDD = approx 2A each fan = approx 0.25A each optical drive = approx 1A What do you do that you need 8 HDDs? And what's the capacity of these drives?