No video signal
(Monitors may also do this, and state Power Saver Mode, or Sleep Mode; instead of No Signal)
1) Check the monitor cable. Has to be ruled out before going on.
Either use it on another known to be working computer, and monitor; or use another known working monitor, and cable on your computer.
Monitor cable checks out go on
2) From here the logical assumption would be to check graphics.
If the graphics are coming from the motherboard, Integrated Graphics; then use a graphics card.
If the graphics is from a graphics card, use a known to be working one, for a test.
[ The I/O area is on the back of the computer. I/O stands for Input/Output. It refers to the Input and Output devices that are connected to the computer; in the rear area.
Mouse, Keyboard, Monitor, audio cables, etc.
If the monitor is connected in the I/O area, the computer is using Integrated Graphics. In the past we used to refer it as OnBoard Graphics.
ON the motherBOARD.
If it is a graphics card being used, it will be in one of the horizontal expansion slots, on the back of the computer ]
However I would like you to jump past that.
1) Is the computer dirty inside? If the Processor overheats it turns off.
(BIOS turns it off) This is a fail safe feature built-in. Keeps the Processor from burning up. (Literally)
Clean the inside of the computer out with a can, or two of compressed air for computers. Use Q-tips, and/or small soft brush (Makeup brush?), to dislodge the heavy 'Gunk', so the air can remove it easier.
2) Ram Memory:
Remove all ram memory modules. ('Stick') Clean the gold plated contact pins with a pencil eraser.
If you are using an eraser on the end of a pencil, and not a solid eraser; refrain from letting the metal band of the pencil, touch the gold plated contact pins.http://en.wikipedia.org/wiki/File:Generic_DDR_Memory_%28Xytram%29.jpg
Handle the ram memory module by the BODY.
The Body is everywhere on the ram memory module, EXCEPT the gold plated contact pins.
The Body is coated with a see-through protective plastic.
Rub up, and down, and across; on EACH contact pin, BOTH sides.
Use air to remove the eraser dust. You can use a can of compressed air for computers, if available; or air pressure from your mouth will be sufficient.
3) Power Supply:
There are two main issues for desktop computer failure;
A) The computer is dirty inside
B) Power Supply failure
Ram Memory contact pins cleaning is an add-on; but necessary.
With a Power Supply having a weak voltage power rail, you could see LED's light, and fans spin; but NOT have enough power to turn the Processor on.
1) If ALL of the LED's (Light Emitting Diode) 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 from 51 to 125 Watts of power.
Just depends on what Processor it is.
That is why you can see LED's light, and fans spin, but no signal.
Use a KNOWN to be good, Compatible power supply; for a test unit.
Use a multimeter to test the 3 main voltages;
3.3 Volts, 5 Volts, and 12 Volts. All are DC Voltage. (DCV)
[In comparison two D cell flashlight batteries produce 3 Volts DC ]
For additional questions please post in a Comment.