Do you have a multitester? First thing I would test is that you are getting the rated voltage on each line out of the power supply. If possible, while under load. If that all looks good, your next step is probably a recap. I'd start with the analog board and see if that fixes things up for you.
Another test to see if it's a power issue is to disconnect the power to the internal hard drive and floppy drive, and see if the machine will boot as far as the flashing floppydisk symbol. If that works, then yes, it could be that the PS is not supplying enough power to boot with everything attached. Then power down, hook up the floppy and try to boot from a Disk Tools floppy, or alternatively, leave the floppy detached and try to boot from the HD again. Or, if you have one, boot from an external, self-powered SCSI drive (CD or HD).