I purchased a used eMachine computer from CompUSA auction site for my folks.  It has worked fine since November, but yesterday they turned it on and NOTHING.  When pressing the start button, both the case fan and chip fan come on.  It will not turn the monitor "ready" light from amber to green.  I tried a different monitor and thats not it.  I opened up the case and checked all the connections for tightness, to no avail.  Where does one start checking out what this could be.

Thanks for any help.

   If the computer does nothing but run the fans, I would suspect a bad power supply.
   If the computer starts and makes a series of beeps, I would suspect a bad motherboard or RAM memory.  The beeps actually are given in a certain pattern which tells what is wrong.  Some manufacturers of motherboards publish the beep patterns on their website, some don't.
   If the computer starts and makes the same noises that it always makes when it starts normally except that the monitor does not work, I would suspect a bad video card, driver, or monitor (which you ruled out).

Is there any way to test the power supply with a meter?  

Also, don't the fans get there power from the power supply?  I would have thought that since the fans are working, the power supply would also be working.  Just a thought.

Thanks,

   Yes, you could test the power supply with a meter but some problems are not detected with a meter (like when the power supply shuts down after a certain amount of load).  The voltages of the outputs are written on the power supply unit.
   It is usually easier just to put a working power supply unit in to see if that is the problem.
   It all depends on where the problem is in the power supply as to whether the fans run or not.

There are 6 voltage outputs from newer power supplies, 7 outputs from older supplies. The -5 volt output was dropped from newer versions, since it was used only by the ISA bus, which is no longer used on new computers.
You can buy a power tester at most computer stores. You plug the 24 [20 on older computers]pin connector to the tester and then you can plug in each type of connector to see if its output is OK.
I would also say that either the supply or video card isn't working, since you are receiving no beep errors.

I took it to s computer store and they tested the machine.  It turnes out to be a fried mother board.  This machine is now used for spare parts.