Moving sucks. When I moved, every fan and the CMOS battery died in one PC and checking my UPS, four that I checked wouldn't power up. That leaves me three that may or may not be viable as soon as I locate which box I put them in. So basically speaking, I have no functioning UPS and my only functioning PC is my laptop

That said. It would be helpful if we knew what model motherboard you have.
Without knowing, there are a few things you could check. Take a really bright flashlight and look down into the PCI slots. Look for any inadvertant crud that may have got trapped down in there, such as hair or dust bunnies. Clean them out if you find any, I prefer using those plastic toothpicks you can get from the pharmacy department. Be sure to take great care not to bend any of the pins which you should also be looking for.
Another thing you might check is the BIOS settings. I have an old IBM Aptiva that would refuse to utilize any additional card on the PCI bus until the onboard hardware was disabled. For instance, a PCI video card would not work unless I disabled the onboard video. Same went for the onboard audio.
Bizarre enough, the same motherboard has settings to disable individual PCI slots. No idea how that's useful, but check for something similar on yours. You didn't specify what model you have, but I did find one "antique" board that used jumpers to accomplish this. I think it's really unlikely, but check your manual just in case. A jumper may have gotten loose or fallen off during the move causing problems.
I don't remember if the PCI specification calls for some sort of fuse but check the board traces and components for burned out parts. Unlikely, but it wouldn't hurt to look the board over. Check the cards for damage as well.