Vic-
It's not a question of cables or adaptors, it's a question of incompatible signals.
There are more details here--
http://discussions.apple.com/thread.jspa?threadID=2205633&start=30&tstart=90
--but the basic problem is that you need a DisplayPort signal to drive the iMac monitor. You can convert a digital DVI output (or HDMI which is the same thing with audio and a different physical connector) to DP format with an expensive converter, but there is no way to convert an analog VGA signal to DP format. The cheaper but more complicated solution for a PC with DVI output, and the only solution for one with VGA output, is to replace your video card with a DisplayPort or Mini-DisplayPort card. Mini-DisplayPort has the same signal but a smaller physical connector.
This was not actually Apple being arbitrary: DisplayPort is more efficient and less expensive than DVI/HDMI because it dispenses with a lot of the conversion hardware needed for that format. Therefore Apple couldn't provide DVI/HDMI compatibility without increasing the iMac cost substantially.
-JAFDC