A hard reset is accomplished by pressing the power and home buttons at the same time and holding them down (no rapid pressing) until the Apple logo shows on the screen. The logo should show within 12-15 seconds. If it doesn't show up within 20 seconds the phone has a bigger problem. The next step would be to try to restore the phone by connecting the phone to iTunes and putting it into DFU mode. Look on Google for the directions for putting your particular phone model into DFU mode. The steps are a bit complicated and may take several tries to get it right. Failing that, the last resort would be taking it to Apple but I wouldn't get my hopes up.
Let us know how it works out for you. Good Luck.