Many thanks to everyone, especially osprey4 & RoHe for so many helpful suggestions. But most special thanks to froggyjo for remembering to post the solution to the issue.
My last post to this forum was that I had ordered the video card that froggyjo recommended. A few days after that, the hard drive crashed. I had a local tech come out to diagnose the problem the computer was having and he was plugging and unplugging all kinds of cables internally in the computer. At one point, he had connected the video connector at a different external connector not on the card and also had removed the card and the computer had started in one try. He also seemed to think that the hard drive had been causing the 3 start issue. I went out and bought a new hard drive two days ago and got it installed and got all of the software, files etc. partially added to the hard drive, but the 3 start issue was still present. The new video card, Nvidia GeForce 8500GT arrived yesterday and I also installed it yesterday and now the 3 start issue is no more.
I know this is old, but I had the same issue start about two months ago. I have 8GB of ram two different sets of memory (this stick look different). It's the same memory all four sticks are dell recommended for Dell Inspiron 530. When I run the dell system config utility online it was only showing dimm 1 and 2, so I moved the memory around grouping them 1 and 2 same manufacturer and 3 and 4. Put newest in 1 and 2 and oldest in 3 and 4.
Just moving the memory around solved the problem, but I have a aging system and the network port is going bad. So I am looking for a cheap (new) replacement motherboard. I might have to go with a different case, cpu, and memory. Fortunately the power supply, video card are new and I can reuse them.