Dropping your laptop from a small height is almost certain to result in some damage; the amount of the damage is going to be dependent on many factors and will be analyzed in this editorial.
If it had been dropped on the corner or edge then you are more likely to see cracks in this area, however, cracks and chips are more likely to be seen almost anywhere around the case. These are the obvious signs of damage. Cracks usually only affect the appearance of the laptop and shouldn't alter or affect the performance so can usually be ignored, however they indicate that the laptop has been dropped from quiet a height and further hidden damage maybe present.
When a laptop is dropped or banged when turned on then the hard disk will almost certainly be damaged. You will most likely see any of these symptoms of this:-clicks and banging noises, operating system not seen, crashing during operating system load, very slow operating system load, very slow laptop operation. If you see any of these symptoms then the hard drive has probably been damaged and will require to be replaced immediately. When you've got important data then recovery must be attempted quickly as the more it is used when damaged the less likely it's to permit data recovery. The harddisk is usually only damaged when turned on; when off the heads park which protects it from minor bangs, however it suffers a large knock then damage can still result.
Check the screen; if you observe any cracks, lines or bars down or across the display, blotches or what looks like ink leaking then the display may be damaged during the fall. A damaged or cracked laptop screen can never de repaired, your laptop has to have a new display fitted by a laptop repair company as it is just too easy to damage it during replacement.
When a laptop is dropped on its power connector, often the internal connections in the connector are damaged. Sometimes it's easy to see where the connector breaks or is bent. Often you'll discover that the laptop no longer charges the battery or works on mains only power where the inner power connector may be damaged. The power connector jack may get very hot in use; this also indicates a faulty connector.
If you have checked for noticeable damage but still your laptop will not power up then it is possible a RAM chip has come loose from its socket. Most laptops have a small RAM inspection door on their base, often secured by a number of small screws. Remove this door and remove and reinsert the RAM chip or chips.
Assuming you have checked all of the above hints and still your laptop doesn't power up properly then there could be a fault on the motherboard. It is mounted inside the laptop case. The motherboard inside a laptop can easily be broken when subject to dropping. Copper tracks may break or electronic components could be broken or cracked when the motherboard is stressed. Only a specialist laptop repair company can repair a broken laptop motherboard; alternative a replacement motherboard will be required.
Always treat your laptop with great care as it is extremely easily damaged resulting in data loss and repair. It isn't a good idea to work with a laptop on your lap as it could drop when you rise quickly!