Thank you Gentlemen, (Tallon41 and HFCG)
Alex,
Please take HFCG's cautions about danger from leaking capacitors and danger from "figiting" with live wires SERIOUSLY.
At this point, it would make no sense, and would be irresponsible, for WTT to make any recommendations other than —
"STOP using that Machine Immediately"
Turn it off and unplug it now.
Given your previous statements about reluctance to do work inside of the case, it would be best for you to have another more experienced and competent individual perform any additional work inside the case.
I would recommend turning the job over to a paid professional.
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What of "future options"?
The Hard Drive can be removed from this faulty machine and installed as "slave" into one of your other machines for purposes of Saving your data and media.
If the Optical Drive (CD/DVD writer) in this machine is of better quality than what you have in your other machines, then you may also want to transfer it to the other machine for use in burning your CD/DVD's.
Next,
Have a Professional remove and replace your MotherBoard.
Have the Professional also install a new Power Supply Unit.
If you have the Professional install the "exact" same Motherboard, it "may' be possible to just pop in the same Hard Drive that you are presently using and have it up and running as before.
Otherwise you may need to reinstall the Windows Operating System.
This "would not" be a Repair Install, but rather a Fresh Installation that would cause the loss of your applications and saved data, so be sure to get your important stuff saved using another machine.
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I'm going to quote some additional comments of caution that HFCG transmitted to me.
Again…. Take these cautions SERIOUSLY.
Hi Doug,
The swollen, leaking Capacitors, with the information of a voltage spike to the video card, indicate that a power fluctuation has caused a great deal of damage to the electronic circutry {motherboard, riser cards)
The unusual memory speed is an indicator of a damaged chip set.
The problems are only going to get worse with time.
The cable to the video card having to be played with is dangerous! There is an electrocution risk here.
The processor may be salvagable, but the motherboard needs to be replaced, along with the video card, and RAM. (the RAM may be salvagable, but it would be better to replace it in the long run).
Trying to repair the motherboard after such damage is a long shot by a skilled electronic technician, cheeper to buy a new one.
Capacitors have a liquid electrolyte in them. This is an acid and is capable of causing burns.
When the voltage spike hit the motherboard the temputers in these caps where high enough to cause the electrolyte to expand, swelling the caps and causing leaking (capacitor bleeding).
This was a major power spike.
The OP is playing around inside the case, and could get some of the electrolyte on his hands, and then rub his eye… causing burns to his skin and possibly his eye!
If a cap explodes while he is playing with the machine he will get burned.
OK, Thanks again Gentlemen.
Alex, we are done now with this machine.

Further use of the machine could result in rupture of the capacitors, leakage and possible burns to objects and people.
Continued operation of the machine with the faulty power connector to the AGP could cause fire and/or electrocution.
Further work on the machine would be far to dangerous to be attempted by other than an experienced professional.
Alex, I'm glad you've decided to become a member here at WTT.
I believe that your post here is very likely to help others who read it and learn from your experience.
I look forward to you being around WTT Forums as need and interest makes that possible.
Best Regards,
Doug