Dell Inspiron 530 intermittently (most of the time) wont start

I have managed to get the computer started a few times after I have unplugged and replugged the power supply or other internal connectors.  Once the computer is started, it will run fine and even reboot, but once it is fully turned off I am lucky to get it started each time.  I have checked the power supply (which is only a few years old) and it tests okay.  I replaced the cmos battery after I had disassembled the computer (for parts) and found it dead.  After getting everything back together, I thought the problem was solved when it booted up, but once turned off, it would not restart.  When I press the power switch, it glows yellow, but only so long as my finger is pushing on it.  The fan pulses as if trying to start but nothing else happens.  Solid green light on the back of the power supply.  I am wondering if it is the power button and if there is a way to bypass it (like hotwiring a car) and hoping it is not a motherboard issue.  It is not currently connecting to the internet but I am not sure if it is because it is too far from the router (laptops are at the same distance and working) because I am reluctant to unplug it and move it in case there is an internal diagnostic I need to do with the computer on.  No recent updates, the computer had been hardwired to the router previously.  I am running windows 10 on the machine.  I am hoping after this long-winded explanation, something will be obvious to someone who knows more than I do.

Thanks