I plan to be travelling to the United States from Europe (the Netherlands specifically) and want to bring my computer. I measured it and it exceeds the dimensions for hand luggage. I'm worried that if I put it in my trunk that it'll be damaged by the rough treatment luggage receives. What would be the best way to ship my computer without having to worry that it'll be dropped from a few feet height (like regular luggage is).
It' probably cheaper, safer and more convenient if you just take your harddisk with you and get another Computer in the USA. shipping the whole box is not a good idea. You would have to remove and single-box all "snap-in" parts and parts attached to the mainboard like ram, videocards, cpu cooler and also hdd and cdrom because they WILL fall out at some point during transport.
Try to fill up your mostly empty desktop with some Styrofoam warped into plastic bags to prevent the mainboard, fans and everything else left inside from moving around.
It's not very convenient but (assuming it's a desktop) I would disassemble it into parts and box them individually. I brought a desktop myself from Portugal to the Netherlands this way (in my checked in luggage) and it was fine, nothing was damaged.
To be fair, the only thing that's at risk from the tall falls and such is the HDD and I guess you can carry that one in your hand luggage. If you have an SSD, even better since it doesn't have moving parts.
As for the rest, it doesn't really matter that much.
Don't forget that if you ship it with a courier, they might charge you customs fees in the US...
Hope it helps!
Call the airline and ask - there must be procedures in place for people who travel with unwieldy but fragile pieces of luggage. Musicians travel a lot, for example, and a guitar is neither hand-luggage-shaped nor sturdy enough to be thrown into the cargo hold. It'll probably cost extra, but hopefully not as much extra as buying an entirely new computer on the other side of the ocean, or having the motherboard damaged in transit.