You did a good job of pic taking. I wish I could say I saw something wrong.
I agree with you, I see nothing visible. And most time you can see something wrong visually,
unfortunately not always. It's also possible one of the switching regulators has just failed with no
visible failure. Using Imgur is just fine with me BTW.
I think it's time to get a meter. Wherever you see large areas of copper that the negative sides of the
Silver cans, (Electrolytics ) connect to, or the marked side also negative. Find a easy spot to hold your meter negative probe
to, with your left hand, then with your right hand, Assuming you are right handed, move the positive probe around to find the voltages
we know are supposed to be there. We have established +12v is there, now you can check for 5V and 3.3Volt. The fans should be at 12 to 12.5V, If less
than 12V, that could still show a problem.
I saw some capacitors marked with a voltage less than that, probably part of the data buss lines to and from memory
and CPU. DAMN! I really wish we could have found something easy with the electrolytic caps, but I guess that would just be too easy!
I sincerely doubt this has anything to do with the issue, but you can pop out the coin cell battery, if below 3v, it needs replacement.
With batteries 1/2 voltage does not mean 1/2 the life left. It means long since dead.
Do you know anyone you can borrow a meter from, to spare you the cost of buying one? Getting one of your own would be more useful
than you may think though. Start with checking the easy voltages, like the connectors to the DVD, 12V and 5V, and USB connectors have 5V.
Kinda stuck till a meter is in play. I'll give this some more thought as to what else can be checked.