My fairly new PC (assembled from parts) crashes regularly. Often this is associated with touching something on the desktop chassis--like plugging something into the speaker outlet in front, or putting in a USB stick. When it crashes, usually the screen goes black although I can still hear the fan running. I can do a hard shutdown and reboot and everything is fine.
It seems like maybe there's a short in there or something? Any ideas?
You did use the stand-offs (spacers) to install the motherboard into the chassis, didn't you? And tidied away the unused power connectors so that they cannot accidentally short to the chassis if the chassis is moved a little bit by, e.g., plugging in a USB stick?
This does not sound like a short inside. It sounds like static electric charges causing electrical surges or "noise" signals. Check to be sure the power outlet you are using has a good Ground connection, and that your power cables and any "power bars" or "Surge Protectors" maintain the ground connection.
If you're somewhat "electrically inclined" you could do two types of check tests. One is to get one of those outlet checkers you plug into any outlet. Its light pattern tells you things like whether the Ground is OK, whether the Hot and Neutral lines are reversed, etc. Use it to check the wall outlet and any wiring devices between the wall and your PSU cord. If you have a resistance meter, unplug the computer and check that the plug's Ground (longer round) prong actually is connected through to the computer's exterior case and to the exterior shell of audio port connectors, etc.
If you assembled the system yourself, think about how you mounted the mobo in the case. There are 5 or 6 (usually) metal standoffs placed in particular locations (according to your mobo) in the case, and the mobo is mounted to those with screws. Some people also place insulating washers under those screws (because mobo parts bags have some) in the mistaken belief that the mobo cannot be connected to Ground (case). It actually SHOULD be connected to the case by those screws - the mobo and / or screws often have little bumps on their surfaces to ensure really good contact.
One last uncommon thing. Do you have any peripherals, like printers etc., plugged into a DIFFERENT wall outlet from the computer itself? On rare occasions this sets up odd small-voltage mismatches between circuits that can cause trouble.