I just got a hold of a different motherboard, which got me to a couple successful startups before the same problem developed. The motherboard came with a full set of RAM, so I'm going to try swapping that in to see if my memory's bad. A new power supply is on the way, so I'll see how that goes.

Some of you are saying the hard drive is bad. I don't have any other SCSI disks to test this with, so could I check it out by simply unplugging the SCSI cable from the motherboard and trying to start it up? I can't do much in terms of software checks because in the few cases where I can the Quadra to start up completely, it locks up within a minute of loading the Finder.