As an "old-timey" hardware tech , I would be asking for more info about the dropping incident .
Was it powered up at the time ? , was the battery fitted ? , was the charger plugged in ?
Will it boot with battery only ( no mains ac ) ? will it boot
without the battery ?
Had any random shutdowns ever been seen before it was dropped ?
Five minutes spent asking those type of questions have saved me many hours of work in "exploring" (ie . checking/ testing everything )
I'm thinking of the components that are most vulnerable when a laptop is dropped :
- the parts that are heaviest take the biggest physical hit .... battery pack , HDD , screen .
- a power cable getting forcibly ripped-out can often damage the soldered connection where the internal socket meets the motherboard.
From what you wrote , my feeling is that it's more likely a power fault rather than a RAM fault .
I would check the power-brick ( ac mains adapter ) with a multi-meter ;
the label says what DC voltage to expect ( and it will be usually read a little higher than this )
re. testing the HDD with a boot disk ; I would have done the same as you, and if it wouldn't run I'd put the drive
in an external case ( caddy ) and then check it using another computer , with something like HDSentinel or CrystalDiskInfo
That all depends on what you have available ... or just lying around ...
Some of this might seem like " stating the obvious " , but it's just the way my mind works ...
Good luck !