Go to office supply store and buy a roll of the big bubble bubble wrap. (not the smaller bubbles) and some packing tape.
Start by getting a large bag (large garbage bag, recycle bag, etc..) this will keep out any water or moisture in case weather happens to get to the box (will not protect from flooding!)
Put your PC in the bag, pull the bag snug at the top and roll it closed as tight as you can. Tape down the portion you rolled-up to the bag surrounding the pc. You can even double wrap it if you want!
Now lay down a length of bubble wrap long enough to make it around the PC with a little to spare, wrap that around the PC and secure it with tape. Wrap it 2-3x more, rotating between wrapping from top to bottom, then front to back. Use as much tape to make sure the bubble wrap wont come lose or the PC wont come out of the wrap. when your done the PC should be minimum 2 layers of bubble wrap all over the PC. You should feel confident that you could almost drop it without damage.
Now, find a box that is a little bigger than your bubbled-wrapped pc to allow for some extra packing. Take some packing material (packing foam, newspaper) and put some on the bottom. Lay your PC in the box and put some more packing material as evenly as possible around all the sides. Now cover the top of the PC, so the box is pretty much full of packing, restricting movement.
Make sure to seal the box well with your packing tape. Go over the bottom a few times where the two flap join and make sure to come right up the sides a few inches. This helps the bottom from wearing or giving out. Doesn't hurt to go over the edges to help reinforce them so they dont accidentally tear. Once should be adequate for that.
As suggested above, ask the shipper for some Fragile labels to stick on the box, as well as, write fragile with a large sharpie a few times on the box.
I wouldnt worry about removing any of the components if you follow these instructions. If you feel better about it, then do it, but the PC should be ok.
You could pack the inside of the PC, but depending on how much space you have inside, it may not be that effective. I receive hundreds of shipped PC's from HP, Lenovo and there is never any packing material inside the case.
Good luck!Edited by Addictedtokaos - 5/28/13 at 1:01pm