Yes it would seem like the psu is at fault. To be sure try again but with the graphics card not inserted, only one stick of ram, no hard drives, no fans connected (except the cpu fan), then see if you get all four phase lights to appear, then after that the cpu fan should continue spinning with all the phase lights still on. If that happens then it would be a good indicator that you are underpowered.
I would never run a system with a cheap and nasty psu. Most cheap psu's stated wattage is what it peaks at and not the lowest wattage like good quality one's, they also use much larger better quality capacitors. My brother had such a poor quality psu in his system, when it died it took out all the other components with it
