Dell Inspiron 530 starts up 3 times

For the past several months, my 5 year old Inspiron 530 has had the following issue:

From a cold start, it will power up for a few seconds (loud fan noise), then power off, then power on for a few seconds, then power off, then power on and proceed as normal.  So from a cold start it will start up a total of 3 times.

When the computer is restarted, it will power down, power up for a few seconds, power down again, power up and then proceed normally.  So from a restart, it will start up a total of 2 times.

I have tried the following fixes and so far none of them have resolved the issue (these may not be in the correct sequence):

I contacted Dell Support.  They told me it was a "software issue" and they proceeded to try several different things over a remote connection.  After about 5 hours of trying to resolve the issue without a solution, I was told it was not a software issue but a hardware issue and referred me to the hardware tech support group.  The technician from that group told me that it was a software issue and that I needed to reinstall the operating software.  Since I also read on the internet that this could be a power supply issue, I had them refer me to Dell sales who could sell me a replacement power supply.

I bought the power supply and installed it, but that had no effect.

I bought a new video card and installed it, but it had no effect on the restart issue and actually caused additional problems.  I removed the new video card and reinstalled the old video card.

I contacted Norton about doing a remote virus removal.  I had two different technicians from Norton work remotely to fix the startup issue, but they were unsuccessful.

As a last resort, I decided to go ahead and reinstall the operating software which is Windows Vista Home Premium 32 bit.  I actually reinstalled the operating software twice, because I didn't reformat the C: drive when I did the first reinstallation.  I did do the reformat of C: drive on the 2nd reinstallation.  While my Inspiron 530 now boots up much faster and also runs much faster, it will still take 3 starts to get going.

So if anyone out there has any insight on this issue, whether it is a fix or whether I should just let it be and not be concerned about it, please respond to let me know your suggestions.  If additional detail is needed, please let me know.