North Pole -
Try this exactly:
1. Turn LED Alert off.
2. Press Home.
3. Press Power+Home buttons at same time and keep both pressed until the apple logo appears during startup. Letgo.
4. Go to Settings/General/Accessibility/
5. Find the LED Alert option that shows its self switched off.
6. Press and hold on the LED Alert's Off Switch.
7. DRAG THE SWITCH to the ON position.
8. If your custom vibrate setting isn't turned off then:
9. Like #7 DRAG the custom vibe switch to the OFF position.
10. Press HOME BUTTON.
Now have someone text you or set a one minute alarm to check it.
Two or more of the 10 steps fix the problem. I don't have time to narrow down exactly which ones. I did at one point have the LED Flash Alert and Custom Vibe on and working together, I'm almost positive. So if you get it working and like the custom vibe feature then try turning the vibe back on via dragging (not pressing) the switch.
GL and let me know if it works or not.