The problem you are running into that is causing the stop errors is the fact that the chipsets are different between the two motherboards. With that chipset difference, Windows is getting confused (it sends commands to the board, but doesn't get the responses it expects) and giving the STOP errors.
If you can boot to safe mode you should be able to load the correct chipset software for the C610, at which point you can restart and then load the drivers for the rest of the hardware. Unfortunately, I am not sure if that will work or not (it depends on exactly how far into startup Windows gets before it errors).
If you can boot to another device (CD, floppy, memory key) you can format the drive and it should then work fine in the C610. From what you describe, I suggest going into the BIOS (F2 at the Dell splash screen shortly after powering on) and double check the hard drive and/or optical drive (CD) are set as boot devices (some older BIOS settings do not have the CD set as a boot device by default).
If you have any other questions about this, or my suggestions, feel free to contact me at [email protected]
(please add 'ATTN: Larry' to the subject to make sure it gets to me).
I hope this helps you get things working.
Dell Customer Advocate [email protected]