1. Could very well be the power supply (PSU) clicking. This could be caused by a bad PSU or by some other part in the system shorting and taking down the PSU.
2. Standard debugging is to remove video and memory and all USB devices and pull all the wires off except the MB and power supply except the 4/8 pin MB power and the 24 pin MB power and the CPU fan. Then see if it starts and indicates "no memory".
--- If it shows "no memory" add parts back in 1 at a time until it stops posting. The last part is suspect.
--- If it still clicks with jsut he PSU, CPU, MB and CPU fan then try a PSU swap.
3. NEVER EVER buy a $30 PSU. "There are powersupplies on ebay and amazon for like $30-$50 depending on the wattage." Instead looks at...