It sounds like your system isn't POSTing (Power On Self Test). Basically this means that one of the pieces that are absolutely necessary for the system to work isn't working.
Check the following:
Make sure that you have a keyboard plugged in. A few systems will not post unless there is a keyboard present (very rare).
Is your CPU connected properly? If it is a slot CPU, make sure that it is all the way click-locked into place, you may have to push a bit. Also make sure that your CPU fan starts turning when the power goes on, some boards wont POST if the CPU fan isn't turning.
Is your RAM in properly? DIMMS should be pushed down on both ends until they click. If you have more than one, try removing all except one and making sure that it is in correctly.
Is your graphics card pushed all the way into the slot? This is a fairly common problem, you need to make sure that the card is fully into the slot, push down on it and see if you can get it in further.
Are any of your HDD cables on backwards, i've had systems that wouldn't POST when the IDE cables were on backward. Try to disconnect your hard drives IDE cable.
If none of the above works, i suggest that you disconnect everything again, then put back only the CPU, RAM and graphics card and see if that works. If this base test works, keep adding stuff back one by one until you have your system all together (or you find the faulty piece).
Good Luck,
Daniel