To me from the indications given it looks like a Power Supply problem.
At first LED lights light, and fans spin.
Then you plug a PCI Express card in, and NO fans spin.
PCI Express graphics card took all the power there was available.
[ A PCI Express x16 slot can deliver Up To 75 Watts ]
1) If ALL of the LED lights were on at once, they would use less than 1 Watt of power.
2) EACH fan uses 2 to 3 Watts of power.
3) A typical Processor can use 51 to 125 Watts of power.
Just depends on what Processor it is.
You don't have enough power to turn the Processor on.
Fans were spinning, you plugged a graphics card in, fans do not spin now.
Power Supply has a weak voltage power rail.
(There are three; 3.3 Volt, 5 Volt, and 12 Volt)
HOWEVER, the method is to diagnose; not parts changing.
Do you have a multimeter to test the three voltage power rails?
I can guide you. An economical multimeter ranges about $5 to $12 around here.
How about a KNOWN to be good, Compatible power supply; that you could borrow from a working computer, for a test unit?
How could a Power Supply go bad from just sitting?
There are Electrolytic Capacitors inside the Power Supply. These have a chemical paste inside. Electrolytic Paste. The paste breaks down over time. Especially if the Power Supply is not plugged into power.
(When an SMPS (Power Supply) is plugged into power, there is a constant 5 Volts present. (5 Volts DC) This is the 5 Volt Standby power )
[The Electrolytic Capacitors used are Radial Aluminum Electrolytic Capacitors ]http://en.wikipedia.org/wiki/Electrolytic_capacitor
Click on the second photo down on the right. The Bottom example is a Radial design. The example is actually a Radial Aluminum Electrolytic Capacitor.
Just so I do not miss anything in the diagnoses, I would also like you to look CLOSE at the Electrolytic Capacitors on the motherboard, too,http://capacitorlab.com/visible-failures/index.htm
Long 'story', I'll try to make it short;
General Electrolytic Capacitor construction,
1) Case: The outside case is an aluminum cylindrical shell.
Think of a 'Coca-Cola' can with the top and bottom open.
2) The top 'lid' is a thin aluminum flat disk.
It has either a lK or X shape cut into the flat disk, partway
It is sealed around it's outer edge to the Case.
This is the Vent Cover.
3) The bottom 'lid' is a synthetic rubber flat disk.
It is called the Bung.
4) Inside are three strips. (There are many layers of these strips in actuality)
A) One strip is metal, and is the Conducting Strip.
It has the Positive lead connected to it. (Lead; Think stiff wire)
B) One strip is also metal, but has a non-conducting medium applied to it. It is the Non-Conducting strip, and the Negative lead connects to it.
C) The last strip is paper-like, and soaked with Electrolytic Paste.
The Electrolytic Paste soaked strip is laid in-between the two metal strips, and all three are rolled up tightly.
The two leads (Positive and Negative) poke down through the Bung.
(Again, there are several layers of this construction, inside the capacitor's case)
When an Electrolytic capacitor goes bad, the Electrolytic paste inside chemically breaks down. It either dries up, or turns into a gas.
The gas expands inside the Case, and pushes against the top seal, (Vent Cover), and bottom seal. (Bung)
The X or lK shape etched partway into the Vent Cover pops open, and/or one side of the synthetic rubber Bung pushes down.
The gas begins pushing Electrolytic paste out.
So much paste loss, and the capacitor can operate at a weakened state.
Too much paste loos, and the capacitor fails.
This is why it can work sometimes, then seem to fail all at once.
This applies to Electrolytic capacitors on the motherboard, and in the Power Supply.
[NOT an invite to open the Power Supply, and attempt a repair!
This = No.
The first thing to do when diagnosing a desktop computer problem, is make SURE it is receiving power, and the correct amount of voltage.
THEN the diagnosis can be continued on.
A Power Supply with a weak voltage power rail, cam emulate all sorts of seemingly software problems.http://www.fic.com.tw/product/motherboard/AMD/K8MC51G.aspx
For additional questions please post in a Comment.