Are you sure it comes from the PSU? If you're 100% sure, you should open your PSU case and check if there's any burned areas on the chip (but do not open it if you got warranty left for it). It should start without the fan spinning too, so the cracking sound can come from electricity bounching where it should't bounche... Remember to check the voltage switch too if your PSU has one.
But still, these things cannot be fixed for 99% of the time so prepare some money for new PSU.
The breadboarding thread has a paragraph about how to build and test a PC in stages.
Breadboard with just motherboard, CPU & HSF, case speaker, and PSU. You do have a case speaker installed, right? If not, you really, really need one. If your case or motherboard didn't come with a system speaker, you can buy one here: http://www.cwc-group.com/casp.html
You can turn on the PC by momentarily shorting the two pins that the case power switch goes to.
You should hear a series of long, single beeps indicating memory problems.
Silence indicates a problem with (in most likely order) the PSU, motherboard, or CPU.
If no beeps:
At this point, you can sort of check the PSU. Try to borrow a known good PSU. If you cannot do that, use a DMM to measure the voltages. Measure between the colored wires and either chassis ground or the black wires. Yellow wires should be 12 volts. Red wires: +5 volts, orange wires: +3.3 volts, blue wire : -12 volts, violet wire: 5 volts always on. Tolerances are +/- 5% except for the -12 volts which is +/- 10%.
The gray wire is really important. It should go from 0 to +5 volts when you turn the PSU on with the case switch. CPU needs this signal to boot.
This checks the PSU under no load conditions, so it is not completely reliable. But if
it can not pass this, it is dead. Then repeat the checks with the PSU plugged into the computer to put a load on the PSU.
If the system beeps:
If it looks like the PSU is good, install a memory stick. Boot. Beep pattern should change to one long and several short beeps indicating a missing graphics card. Silence or long single beeps indicate a problem with the memory.
Insert the video card and connect any necessary PCIe power connectors. Boot. At this point, the system should POST successfully (a single short beep). Notice that you do not need keyboard, mouse, monitor, or drives to successfully POST.
Now start connecting the rest of the devices starting with the monitor, then keyboard and mouse, then the rest of the devices, testing after each step.
+1 for run it in a bare minimum config to rule out as many faulty components as possible, although it can still be a faulty PSU if it powers on with bare minimum and is dying under load when everything is plugged it. It really sounds like a PSU problem to me though, check if it makes the noise with all the power connectors to your components disconnected. (Mains plugged in of course.) Also, you should NEVER open the PSU unless you know what your doing. The 400V capacitor can hold a lot of power, especially if its not discharging due to a fault in the PSU.
I also have one of those PSU testers. They are great for finding a bad PSU. But because they present a very light load to he PSU, they cannot tell you if the PSU is really good and capable of supporting the load of a complete PC.