What exactly do you mean by "X0" series?
You also said "There are also PowerEdge 2900 (not PowerEdge III) selling functional with the X5450 processors" ... what do you mean "not PowerEdge III"? Only the III revision of 2900/2950 will take 5400-series processors. Any PE2900 I or II that has 5400-series processors installed and working HAVE had the motherboard upgraded. I have not seen any non-III's with 5400's; but there are several examples of III's with 5400's.
Also, I can't confirm until I get to work Monday whether a 2950 III motherboard does not have IDE slots (googling images all show two SATA ports AND IDE) and a 2950 II does not. However, given your production date, and the fact that the III's were released in late 2007, there is no reason to believe you do not have the III board (unless it has been replaced/removed at some point).
All that said, if the processors match exactly (including stepping version), the X5450 should work. Do they work when installed individually in slot 1? You might try clearing the NVRAM using the jumpers on the motherboard ... that is a pretty common fix for validated hardware upgrade issues, especially with RAM and processors.