Loose screw and case frame short...if yer lucky.
 
If you ain't...look at where the mobo power sockets sit in relation to the case standoffs...the supports for the motherboard. Real easy to crack a mobo trace or three seating a tight power plug located in between standoffs where the mobo can flex.
 
Check your warranty if you look at this and still no joy...then open her up and see if you can duplicate the "gravity fault" by moving wire bundles, PCI cards etc. Your playing with fire here, not to mention live juice, but you know about static issues, and what's hot at killing levels and where, or you best take it to the shop and might not wanna build your own to begin with.
 
You also have some sort of protection in or at the power supply. I've seen fuses w intermittant breaks, bad voltage select switches, bad back of PS on off switches, bad front of case power switch relays, shorts where the ISA type plugs in the power bundle sit before the SATA type connectors, and then there's bad mobo power relays, not properly seated mobo power relay plugs, and of course, the notorious pinched or scraped power cable, usually associated with the drive bay.
 
Look at your expansion cards if any. I've seen the edges of PCI or ISA cards barely touching one tall component on the mobo, swapping slots was a permanent fix.
 
I'm no guru, but I've built a score or more for me, including Slack, RH, Solaris, Novell NT and DOS boxes that can be finiky with hardware and PS issues, 50 or more for an airline including HPox and Sun big iron, and tweaked maybe 3500 more on the production floor at HP.
 
You have a bad connection somewhere, and you have one clue about what makes it work or not work. Clear your head and approach at times of low stress, takes some notes as you go along, and chase it out.