Try to turn on computer and the fan blows, but light jiggles and nothing happens. Hard drive shot or processor or ...???

Hi,
Chances are that your power supply is toast.

Although you could try removing either one of your rams (if you have 2), and unplugging any optional device plugged onto the motherboard (Hard drive, dvd player)

In the worse case, your motherboard could be broken and need to be replaced.

Did anything particular happen before it stopped powering up?

sounds like your system is booting up and running due to the hold power shutdown procedure. you might try replacing the video card or adding one if your video is integrated.

Remove hard drive, find out make and model of hard drive. Go to hard drive manufacturer's website and download testing software (if you have another computer with internet access). Should be a bootable ISO file. Burn the boot cd and run it on the host computer after reinstalling the hard drive. Sounds like a bad hard drive in my opinion.

Try cleaning the RAM like shown in the image below.
Hope this helps

Processor may be defective

remove the processor,ram for 30min and put them back

When the laptop freezes up on you does the keyboard or anywhere on the top cover feel very hot if so check to see if the fan is even blowing, if it is blowing then its possible there is dirt on the heatsink fan that is blocking the air flow and thats causing the overheating. You would need to take apart the laptop to get to the cpu heatsink to remove all the dirt.

if the fan isn't running at all then you would need to get a new fan.

If the fan is running and there is no dirt or debris near the heatsink then that means the motherboard is not reglulating the voltage properly and the motherboard needs to get replaced.

if nothing is feeling very warm or hot to the touch and the system is locking up then the hard drive may have bad sectors and the hard drive would need to be replaced.

you can try the memory try one stick at a time. also try the laptop with as little components as possible.

remove the dvd drive, hard drive and wifi card and see if it will boot.

then put each one back in at a time and try it to find the culprit

my inspiron 530 giving me trouble. Blue light is on, but the computer goes no where. Try to start by shutting down and restarting but the start sound keeps coming fora long time and nothing happens. So to say having trouble starting and sometimes it shuts down but the blue light stays on. Sometimes I cann't even turn off the computer by pressing blue light - trouble trouble trouble

Well, it could be any component going bad, in this order: power supply, video card, memory, motherboard. You can try known working video, power and memory if you'd like, but it is probably the motherboard in this particular case. If you look at the capacitors on the mobo, you'll probably find that at least some of them are bulging at the top and/or leaking. the only thing to do if this is the case is to try and replace the bad caps - but this is VERY difficult, even for an expert.