I had problem with my computer from a few months, as it sometimes stopped booting. First it was only rare situations that it didn't start up at first, and after a few try it usually booted. Then it stopped starting definitively.
I decided to replace motherboard, processor and ram as well . Unfortunately it didn't help much. I found that with a new motherboard, processor and ram computer sometimes starts up but most try it doesn't. I mean one try for a 3-4 it boots successfully but if switched off and on again screen remains black and it bleeps endlessly 3 seconds bleeps. Board has power as diodes lit orange, ventilators move. If graphic unit is connected its ventilators also move, and HDDs if connected work also (I can hear their movement), etc.
I removed graphic card and connect monitor to motherboard integrated cards - its the same. Sometimes it start but most times not. I unplugged all other devices (HDDs, DVD, even USB) - still usually not booting. I changed power and monitor cables, set other monitor, and even buy a new power supply - still the same. Now it's virtually new computer - as I changed motherboard, processor, ram and power supply unit, and it still doesn't work correctly. I was unable to install operating system - I tried with windows but after first reboot installation was broken. I have no idea why after replacing nearly all parts (except housing:) my computer behaves in such strange way. Of course I check if there is correct power connection, if there is no screws or other metal parts touching the board, install processor correctly and gently, as same as processor cooler before posting.
In present configuration it consist of all brand new:
motherboard - gigabyte b150m-dv2 ddr3
intel core i5 - 6500 LGA 1151
power supply unit - chieftec force series 500 W
2 x 8 MB RAM 1600 kingston hyperx
1T HDD (now removed due to tests)
The only one used previously part is graphic card ( - GeForce GTX 660 TwinFroz rIII) but now removed due to tests, so it seems irrelevant.
Of course problems with hardware are rather common as same as computers unable to boot, but I couldn't find many posts of sometimes starting up and sometimes not booting at all computers. If the components was faulted I think it couldn't boot at all, the same as if components was not able to cooperating. Moreover similar symptoms had my computer before I started replacement its components despite it consisted on other and previously used parts (of course I think that its coincidence but I'm not sure). Maybe someone on forum meet such situation before and can help:)