Yikes! Are you saying you're pulling and re-seating the video card with standby power present? Even if you pull/push perfectly straight on an AGP card there's a good chance of shorting the pins because of the close-pitch staggered pattern. I managed to cause quite a spark even with a PCI card once.
The kind of behavior you're experiencing should be related to one hardware device/component that is confusing the system. While it may be a sign that something is failing, often it's a mild compatibility issue with RAM or an expansion card, or even just something slightly mis-seated. If I cause a hardware-related freeze and then reset the computer from the front reset button, it almost always does the same thing you're seeing, and then I have to use the internal reset to shut it off first before powering up again. Because of all the crazy experiments I do with hardware I've seen this happen a lot with MDDs.
I'd check pin oxidation and seating of the video card first, replace it with another one second, then look at RAM and any PCI cards third. If you get as far as checking the RAM, install only one stick at a time in the first slot and see how the machine responds. The RAM timing is determined by the first stick in the group, which can result in strange issues with unmatched ones being pushed past their reliable timing limits (no matter what their own actual speed chips say about them). I had one machine working for months, when suddenly one day it insisted one of the sticks was incompatible.