"We make house calls" is our slogan for a reason. Like the victim of a car-crash, computer crashes may be made worse by moving the victim.
Another problem with moving computers to have them worked on is the "jiggle" issue. Say for instance you have a cable with a broken wire in it. By moving the computer, this wire may move enough to re-close the gap, making it temporarily functional again. So when the tech looks for the problem, it doesn't exist... until you take it home and run it for a while, and the wire once again separates!
The most common problem with moving them though, is that most computers have several other devices hooked into them. Quite often, these other devices play a part in whatever is going wrong. For instance, say you have a printer and a camera hooked up to your PC. Everything is fine, until one day your PC stops working. You unhook it and take it into the shop, but it works fine there. So you pack it up and take it home, where again it doesn't work.
You could have to go through this several times before the tech tells you to bring in the other devices. So you bring in the printer (because you almost never use the camera). Again it checks fine at the shop. So you take it home and it fails. So you make another trip, finally bringing in the camera. No point in bringing the printer this time, it's already been checked out, right?
Many PC problems involve what is called a three-way conflict. This is where three items (programs, drivers, or devices) get into a labor dispute and all of them go on strike.
In order to resolve these things, all parties must be present. So unless you have the printer and the camera and the computer all hooked up together, you'll never fix the problem.
Most techs will spend about five hours troubleshooting this sort of issue before throwing their hands up and telling you that it's unsolvable, and that they'll have to re-format (wipe out) your hard drive and restore everything from scratch. This means that everything you've done will be wiped out. A good tech will save your data first - a bad one won't even ask if it's okay before s/he proceeds to wipe out all your hard work.
The sad part is that if all the parts were there, they probably could have resolved the conflict in an hour or two.