It is possible that the power supply isn't capable of supplying enough power when all the computer parts are putting maximum demand on it. The Ebuyer supplies are very good value for money, but are clearly not the best quality. When using such cheap supplies I think it's a good idea to rate them generously. So whereas a good quality 400W supply might be ok for your system, I think a 550W Qtec would be a better bet for a cheap supply click here.
The PC powers up, ie fans spin, then nothing, so the PSU is getting enough juice for this, but no POST beep, just a lot of spinning fans. I'm reckoning that the initial draw is high enough to be causing the problem