It sounds like your phone is on, otherwise the vibrate switch would not be giving you a response.
You need to determine it indeed you have no display at all, or if your phone has display out put, but no backlight. Unplug the battery and plug back in. Clean the screen thoroughly to remove any fingerprints. With the phone held under a very bright light connect a charger to prompt the phone to boot up. If you are able to see a very faint Apple logo than this is a backlight issue, not a display issue.
You will need a microscope to inspect the components near the display connector to see if a filter is blown. It also would be a good idea to look under the screw holes surrounding he lcd connector for long-screw-damage. This would appear as a crescent shaped bright copper scratch on the nearly-black surface of the motherboard.