In fact, maybe I should backup for a minute...
The primary reason I was thinking it might be a good idea to upgrade the  original 220 watt power supply unit is that I want to disable the  original Intel 82845G integrated graphics controller, which is WAY  out-dated (along with the rest of the system I guess) and install a low  watt video card in the available 4x AGP slot : a GeForce FX 5500, which does not draw more than 25 watts when at its PEAK performance.
So, I was introduced to a power supply estimator tool here: 
http://extreme.outervision.com/psucalculatorlite.jsp
The estimator tool recommends 50 watts headroom above the total required  for all devices installed. The power supply estimator also assumes you  are running all installed devices at the same time, which I questioned.  Someone told me that there is one time that all installed devices run at  the same time, which is at start up. He said when you power on a  computer, anything with a motor (like a hard drive) requires 3X the  recommended watts. I was concerned now that I should be adding up what's  installed in my system to see if I might be in trouble if I install the  video card. 
When I used the estimator tool to add up what my system was CURRENTLY  running, I got a recommended power supply unit that exceeded the 220  watts of the original unit.
Basic system:
2.4 GHz Pentium 4 CPU (Socket 478, Northwood, estimated watts below used CPU at 90% TDP)
1 IDE hard drive 7200RPM
1 DVD/CD-R combo optical drive
2 sticks DDR RAM
3-80mm fans
(My modem is externally powered, so I'm not including it.)
152 watts required / 202 watts recommended. 
I considered that the above doesn't include that a hard drive motor  needs three times its estimated running power when it starts up and  needed to add 36 more watts. So now, the required power for the above to  run at startup is 188 watts (152 + 36). With the recommended headroom  applied to this (50 watts) the estimator tool would recommend 238 watts  -- larger than the original power supply unit.
But the above listed devices are not all that are running on my system.  I've got another IDE 7200 RPM hard drive. So now, we should be adding  another 54 to the total required watts if it needs 3x the required power  for startup (18 watts normal running + 36 more for start up). That puts  the total required watts at 242 watts and I'm only running the 220 watt  OEM Compaq unit.
But additionally, I have a PCI soundcard installed. The estimator tool  uses 13 watts as the average wattage needed for a PCI card. Tack on the  watts for my soundcard and I should require 255 watts. The estimator  tool would add 50 watts headroom to this. So now, the recommended power  supply unit should be 305 watts. Yet, somehow, I'm running these devices  using the 220 watt power supply unit that came with the computer. 
So, you can see why I'm concerned about the apparent "need" for a new  power supply unit, but I have questions about 1) why the power supply is  estimated in such a way that assumes all installed devices are running  at the same time, and 2) if I didn't include the power needed for the  Intel 82845G integrated graphics controller originally installed on the  MOBO, which I intend to disable, I may not need much more power if all  I'm installing is an AGP video card like the GeForce FX 5500.
When it came to my attention that a 350 watt power supply unit was  available for not much money (the HEC-350TA-2RK noted at the first post  above), I figured it wouldn't hurt to add some available watts to the  system, or so I thought. NOW, it looks like I opened up a can of worms.
I tried to do what I think is a more conservative estimate of my power  supply requirements. The basic system requirements are still the same,  152 watts.
add 2nd hd drive (+ 18 watts, not including the 3X factor for startup):
170 watts total required
add a PCI soundcard (+ 13 watts, average)
183 watts total required
If all the above devices were running at maximum power requirements for a  sustained period they would need 183 watts. My power supply unit can  handle a maximum of 220 watts, so the demand would not be greater than  what's available. I left out the existing Intel 82845G graphics  controller, but it's not important because it's going to be disabled. If  you now add a Nvidia FX 5500 video card (+ 25 watts at peak  performance) you get:
208 watts total
If this is accurate, I still have 12 watts available from my 220 watt  psu for a very modest headroom, but again, the estimate assumes all  these devices are running at the same time and maximum power is required  from the system. It is highly unlikely that this will ever occur,  unless it's true that when powering on the computer you need to have  much more headroom than 12 watts because all the devices start up at the  same time. I'm also being told that power supply units are made to be  able to withstand a brief surge of maybe 50-100 watts higher than the rated  watts for this purpose, so it's still unclear to me what I actually  "need." 
Someone suggested I get one of those "Kill-A-Watt" meters that you plug  appliances into to see how much power it draws and I'd know what my  system is doing. The meter is $22 -- the cost of some power supply  units!
If I can't get a straight answer about this 12.8V rail issue regarding  the original power supply unit, and given it may be crucial to run the  motherboard and CPU with the 20-pin connection, I may just try  installing the GeForce FX 5500 AGP video card without changing the  original power supply. I was also thinking I could disable my second  hard drive (which is only used for backup) while trying to see how the  system works with the video card installed to see if the power supply  unit stalls or if the system keeps rebooting. Of course, I've already  been told that if the original PSU starts smoking or shorts out suddenly  it could take other components with it, including the CPU. Hence, my  concern for getting a new power supply unit. Funny how all I want to do  is install a video card that needs about 25 watts max and all these  other issues are involved! 
   
Keep in mind that someone else suggested if the motherboard for my  system has 3 PCI slots and an AGP slot the power supply unit should be  able to run devices installed there. Why would they include the slots on  the motherboard with no upgraded power supply available made by Compaq  or HP (there is no other power supply that I know of to fit in the EVO  series except for a 240 watt model in the D500 series)? There was also a  video card that HP offered as an after-market upgrade to run on the  220V power supply, a NVIDIA GeForce2 MX200 64-MB with DVI-I output. I'm  sure they didn't expect users to need to upgrade the power supply unit  to run it, but I do not know how many watts it needed.