I have a Dell Vostros 220 and the cps seems to have burnt up (lots of winds and voltage changes in our neighborhood - and yes I use a power surge proctor)so I bought and installed a new cps and now the light in the back blinks green and there is no noise/fans when I try to power up. Does the cpu need to be hooked up to the monitor in order to boot up?

The monitor does need to be hooked up, although it makes it easier to see if the machine is actually booting.

Please clarify whether it was the power supply or the CPU (processor) that was replaced.

Power supply repair tips:
http://www.smpstroubleshooting.com/

These are some basic techniques to troubleshoot TV power supply