I actually think this has nothing to do with AS since all carriers operate the same way, and it's not conducive to transporting a computer.

Is this for a short trip or a permanent relocation? The best way to ship your desktop computer is to ship it via a commercial carrier - checked bags are not a suitable mode of transportation for desktop computers. If you have the original packaging, that would be best. Otherwise, find a box twice as big as the main tower (in each dimension). Remove the hard drive (it's most sensitive to movement and is the only irreplacable part of the PC) and take it with you in your carryon. Fill the box 1/4 with packing peanuts, put the tower in, and fill the remaining empty space with packing peanuts. Do not skimp on the size of the box or the packing peanuts! Repeat for the printer. Resist the urge to stuff small items like speakers in with the packing peanuts. You need that room for cushioning.

Take the box to a UPS/Fedex store and declare the value. They will charge a small amount extra since it's worth more than $100, but it's the only way to make sure you will be properly reimbursed if the package is lost or damaged.

All the smaller components like speakers can be carried with you in your carryon. Do NOT ship anything expensive or irreplacable in your checked luggage - if it gets lost you will only be reimbursed a nominal amount.