If I just turn the computer off (i.e by clicking on "START" and then "turn off") and then restart her by pressing the "on" button on the front of the tower it'll start up fine.
However if once I've done the above I also switch of the PSU at the back of the tower, when I switch it back on and then press the "on" button at the front all I get is the red and green light flashing and also the fans inside flicker on and off. So then I switch off the PSU again and try the same cycle over and over about 5 times and eventually there's this clicking sound and finally the computer starts up.
First thought is the power supply.
What do you guys think?
Thanks

Turn off the PSU. Then, while holding the power button in on the case, switch the PSU back on. This sort of jump starts some PCs that I've worked on and usually works.

If not, do you have another PSU you could test the machine with?