When CPU is working fine and no problem with it, yet there is no output signal received from the CPU to monitor connected means that some thing is wring either with the connection from the CPU to the monitor, or with the monitor itself. It is not possible to say anything more about the nature of the fault without examining the related hardware and the software.
The fact that the monitor works when connected to another CPU, indicates that the monitor is also OK. In this case it may be a question of compatibility and/or installation of the monitor. If both the CPU are identical and the monitor has been properly installed on both the CPU then the only possible alternative left is that there is some problem in the way CPU and the monitor have been connected.
Of course, the basic assumption that the CPU has no fault may also be wrong. The fact that another monitor does not work on the CPU points to the possibility that the fault is with the CPU. If this is the case than exact nature of fault in the CPU will need to be investigated before a definite conclusion can be drawn about the nature of fault.
its a mother board problem. replace if its in warranty. your mother board is not sending a signal