Is the iPhone charged, if yes try resetting again by pressing and holding the sleep/wake button and the home button for 10-15 seconds until the Apple logo appears, ignore the red slider. Then turn back on. You won't lose any data doing the reset. If its not charged, charge via a wall socket for 15 minutes and then try to reset again. You may need to press/hold for longer than 15 seconds so try this first.
If that doesn't work you may need to restore the iPhone, you can restore from backup on the computer you last synced with http://support.apple.com/kb/HT1414. Otherwise, you'll have to force the phone into recovery mode & restore as a new device. All data on the phone will be erased http://support.apple.com/kb/HT1808.
I had this same problem... twice. This is an extreme case of the phone being stuck in sleep mode. Usually when my phone 'turns itself off' I can just hold the home and lock buttons to hard reset, but in these two special cases even that did not work to get my phone back on. The first time, I eventually gave up and just left my phone plugged into the wall charger. It turned itself back on after about 15-18 hours. The second time (which literally just happened), I solved the case much sooner by doing the following:
1. Place phone in ziploc bag in freezer for ~15 minutes.
2. Place phone in bag of rice for ~30 minutes.
3. Use another phone to call your phone (you'll notice you still hear a ringback as if your phone is on). After each call, try to turn your phone on using the reset method or simply using the lock button.
At this point, your phone should either turn on, or tell you to hook it up to a charger. Hook it up to iTunes just to be safe. If you're still seeing a dead, black screen, take it to the Apple store.