Solved. After trying everything and waiting, I ordered a new Gigabyte MB, put it on a bench, put in my old CPU (i3-2125), my old memory, connected up the power supply, touched the front panel contacts, and it started up correctly. I then put everyhting back in the case and it has been working now for about 4 days. The MB I purchased was a Gigabyte H61M-USB3H-LGA1155 from Newegg for $57.73 incl. tax and shipping. The reasons I ordered this MB were that it would fit in my case, had the right socket so I could use my old CPU and took the same memory that I had. The lowest price I found on an HP MB was $220.
So it was the MB, even though I could see no damage to the MB. I guess I knew something was amiss when I could not set the date in the bios, which was the first time I have ever seen that.
Thanks for all the responses that I got.
Maxgle from CA