On pressing the power button the fans start and the red activity LED on the case flashes for a few seconds, but after that nothing else happens and the monitor remains blank except for a "No Signal" message (monitor generated).
On a normal start up the monitor shows the "Chilllblast" logo momentarily, before going on to the POST screen, etc.
Seems to me that the machine isn't even getting as far as the BIOS.
It is nearly five years old and I was thinking of changing it later this year, so won't want to spend too much on it!
You cannot check a PSU unless it is under load, as you will blow the PSU. You need to Probe the back of the Main PSU plug for Correct Volts when its connected and switched on. These are all low volts no danger in the above
I still think you have a Faulty PSU, if not the CPU is the next to check.
If the Old PSU did blow it can take out CPU and or Motherboard