There are multiple reasons why an iPhone won't turn on not just because the mainboard is dead. I'l start with some of the more basic fixes and hopefully one of the pros can expand on it.
Make sure the phone is fully charged and powered on. Plug it into your PC and see if iTunes recognises it.
If it doesn't it may be in DFU mode. Hold the power and home buttons for 10 seconds then release the power button while still holding the home button. If the phone is in DFU mode it should boot up.
If you have previously opened it up check to make sure all connectors are seated properly and that everything is where it should be (e.g. grounding tabs/screws)
That's a start at least. If you want proper help you will need to be more descriptive about the problem.