As you say there are more than one possible cause of this but if you follow my canned text on cleaning out the inside of your case safely then most of the checks will be done, can I though ask when the PC does actually boot up are the time and date settings correct?
If the computer needs cleaning out, first remove the power cord from the wall and open up the case, take anti static precautions before touching anything inside, you can do this by touching a bare metal part of the case, remove the video card, blow out the slot and re-seat the card securely, do the same with the memory sticks, clean all internal fans, if you use canned compressed air do not let any fan spin freely this can damage them, use something like a clean lollipop stick to hold the fan.
Remove the CMOS battery (see .jpeg) for a few minutes, replace it if you have a spare one and upon first boot you will need to reset the time and date, save (F10) and then Y to accept the changes.
Make sure all internal connections are secure and that there are no loose components, write down the psu details (make and model) re-assemble the computer, boot up and see how it goes.Just a cautionary note, if you do use canned compressed air do not upend the can as it is possible for fluid to be emitted.
.jpeg courtesy of rshaffer61