iMac RAM upgrade madness

My iMac (Mid 2007 aluminum) had been upgraded so that one slot had a 2GB stick and the other had a 1GB stick. A 2GB stick was purchased to replace the 1GB stick, for a total of 4GB.

Unfortunately, they don't work together..

When you have the 1GB stick with either 2GB sticks, the computer boots up fine and registers a total of 3GB. Even if they are swapped places.

When you put both 2GB sticks in (in either configuration), however, the computer boots and only displays a black screen. No chime is heard, but the computer running can be heard.

Any ideas? This makes no sense at all.