A1200 Will Not POST correctly

Hello everyone! Recently acquired an iMac 24" A1200 Late '06 model. Currently will not start. Computer when powered on does not chime and does not have anything come up on the display. The white LED light does stay on though. I thought it was a RAM issue but I tried swapping them it didn't start. So I left the RAM out entirely and it did the exact same thing. Just a white LED light. So do I have a RAM port issue? Or does this model have graphics card issues that cause this problem? Thanks!

@danj Appreciate the answer. The specific one iMac I was asking about had a perfect condition power supply in terms of the condition of the caps. However, the second A1200 I acquired that also was not working at all I had not yet diagnosed. And it would appear that it does indeed have said capacitor problems. So I ordered another PSU on ebay. I have far too much in these two since I have ordered a GPU, SSD, RAM and likely more for the first one. Now this one needs a power supply, an entire LCD assembly that I shipped in from Canada, and then all the things the first one needs. Oh well. Can't let them die.