No, you're not allowed to do that.
Sorry, but your old hard drive is looking for your old hardware. The OS on the old hard drive has no idea how to even communicate with the new hardware. Hence the blue-screens.
You are going to need to either do a repair on the OS by booting from the OS drive or do a fresh OS install (recommended). Since your new motherboard does not have and IDE port, you will either need to get an IDE to SATA adapter or just purchase a new (SATA) Optical Drive.