emachine e625 wont start up, the lights comes on, it just clicks off, the hard drive seem fine?

Test your PSU or replace it if your power supply units fan is not working your PSU is faulty

One bad lead can cause a computer to continue on a cycle or to shutdown or fail to detect/ boot up a computer hard drive

Test all leads that attach to your hard drive including electrical extensions,IDE,SATA

the leads from your "((MOTHERBOARD TO YOUR HARD DRIVE))" make sure they have a secure connection and are not faulty or just replace them they could be faulty
make sure all leads that are attached to your drives dvd\cd have secure connections and are not faulty even the electrical extensions or just replace them they could be faulty a computer needs its connections to continue its cycle and have an end so any faulty leads will end up with a computer erroreven something as small as a faulty electrical extension or fan lead can cause this problem

follow the troubleshooting procedure a computer needs all of the data and electrical current to travel through every device and to have an end to be able work properly

a motherboard and a hard drive any leads between them will fail before your motherboard or your hard drive if its a flat ribbon 40 pin type IDE replace it this will be the first to fail check all electrical extensions make sure they are securely seated even the cd/dvd floppy drives need to have current go through make sure these drives are working hope this helps also it could be a dirty computer clean all of the dust from your computer you could use a vacuum cleaner but whatever you use make absolutely sure there is no moisture gets to anything in your computer