1) Check the monitor cable first.
Use it on another computer, if available. Also try the other monitor, and monitor cable, on your computer. Rule out whether it may be the monitor, or monitor cable.
2) It's a Lenovo 3000 desktop computer, and one of the J series, apparently.
Which one of the J series is it? Just two examples, J110, and J115.
The Lenovo 3000 series desktop computers come with Integrated Graphics.
This means the GPU is soldered to the motherboard.
[GPU = Graphics Processing Unit.
If the GPU is soldered to the motherboard, it is Integrated Graphics, or also known as OnBoard graphics.
ON the motherBOARD.
A GPU can also be soldered to an adapter card.
Graphics adapter card, or usually just referred to as Graphics Card.http://en.wikipedia.org/wiki/GPU
Let's say the Onboard (Integrated) graphics GPU, is bad on the motherboard.
The Lenovo 3000 series desktop computers, have a PCI Express x16 slot on the motherboard, which is used for a graphics card.
GPU is bad on motherboard? Install a graphics card.
Plug the monitor into the graphics card.
(Don't forget to install the drivers off of the CD that comes with the graphics card, First.
Then install the graphics card)
3) Let's also go back for a moment.
No video on the monitor, (Or also can be said as no graphics on the monitor. No Signal), can also be attributed to the fact, that the computer is Not working.
It may seem as though the computer IS working, however.
Lights may come on. Fans may spin, and it may sound as though the Harddrive is operating.
Problem is the Processor isn't operating.
The power of a Power supply is generally rated in Maximum Wattage.
(Voltage times Amperage = Wattage)
[There is one more power factor to consider, when stating the maximum power rating of a power supply.
The Amperage of the volatge power rails, but we don't need to concern ourselves with this at the moment.]
1) ALL the lights use Less than 1 Watt of power.
2) EACH fan uses 2 to 3 Watts
3) A typical Processor can use up to, 51 to 125 Watts.
Depends on what Processor it is.
Using the Lenovo 3000 J115 7387 desktop computer for an example, the standard Processor that comes with it is an AMD Athlon 64 X2 4200+ processor.
(AMD Athlon 64 X2 4200+)
The AMD Athlon 64 X2 4200+ processor, can use up to 89 Watts.http://en.wikipedia.org/wiki/List_of_AMD_Athlon_64_microprocessors#.22Manchester.22_.28E4.2C_90_nm.29_2
No Processor running, No computer.
No computer, No graphics on the monitor (Video)
[The Processor is the 'Brain' of the computer.
No Brain, there is nothing to find the boot sector on the Harddrive.
The Harddrive spindle motor just spins the Platters inside the Harddrive]
The Power Supply may have a weak Voltage power rail, and not have enough power to turn the Processor on.
Just enough power to run the hardware components, that do not use very much.
You can test the Power Supply, or replace it with a KNOWN to be good Power Supply that is compatible, for a test.
Should you wish to test the Power Supply you will need a multimeter, or a power supply tester.