Gateway Vista Desktop- won't turn on

[agavesupreme]

Hi,
I am sorry but I am away from my computer right now, but I will add more specs if it would help-- I searched the forums and found some similar posts but not specifically one with my problem (but if I missed it, I apologize). 
I have a gateway desktop purchased around 2008 and running Vista; I know it has 1TB but do not remember the other specs off hand.
I left it on for an hour or so and returned to find it turned off -- (it is not set to hibernate or sleep).  When I pushed the power button nothing happened - no light, no nothing.
I checked the power cord and found it in working order.
I opened up the computer and noticed that there is a green light in the middle that goes on when it is plugged in -- so I think that is an indicator that it is getting power.
My questions are: could there be a connection that came apart and if so what might me an obvious place to look?  If something was "burned out" and needed to be replaced, what would the likely culprits be?  If I cannot "fix" the computer is there a way to recover the software on it by removing some of the insides?
As you can tell I have less than a rudimentary knowledge of computers, but I would like to try to fix this on my own if possible ... any help would be greatly appreciated and please let me know if you need more info -- I can also take some photos of the inside and post them as well if that might help.
Thanks!!!

[agavesupreme]

Some pics for additional info:


[year+ old attachment deleted by admin]

[Popeye67]

could be several things, first thing i would do is check all the connections are good and any add on cards are seated correctly, then i would swap out the PSU for one you know is working.

[Raptor]

The pictures are pretty low-resolution but judging from the first one your CPU cooling system is completely caked with dust?

There's your problem right there ...

[agavesupreme]

Thanks- I noticed that one of the fans had fallen off when I opened it up.  I am guessing that this caused something to overheat, but I am trying to figure out if there is one problem area more likely than another.  I cannot see anything obvious and all the connections are intact.  There is simply no response- no noise, no fans, nothing when I try to turn it on.
I opened up the power switch and it looked like a connection was a little loose, so I disconnected and re-connected it.  The only difference is that now the blue power light stays on - but there is still nothing coming from the computer - no other "life" except the green light glowing in what I think is the motherboard.
I am guessing I will need to take out the hard drive and transfer the files to a new computer but if there are any other ideas worth trying, please let me know.
Thanks!
PS- my computer is a Gateway GM5632E and I can post more photos- closer up if it might help.

[Raptor]

You opened up the power switch? What exactly does that mean?