Ah... Old iMacs :-)
There are like only four serious causes of trouble with iMacs I came across the last two years:
1) Bad backup-batteries causing a forced PRAM reset (means dismanteling the machine and push the tiny button on the motherboard). Can make the computer start into a black screen.
2) Bad fly-back transformer on the monitor. Easy to repair if you know how to solder. Makes the computer to not start at all.
3) Bad harddisk (causing booting problems ending up in the firmware).
4) Dust and sigarette smoke creating bad contacts.
All four problems are rather easy to solve. Binning can be done any time ;-)