This PC I'm on has been acting up in the same manner.....sometimes won't power on. Did it just today, as a matter of fact. Generally, it's a connection issue. We did recently change the PSU in it, but I had to unplug the main power harness connected to the motherboard and plug it back in. That fixed it....this time. Sometimes you will have to re-seat cards in the system too. The connections get cruddy and the re-seat sort of scrubs the contacts back to a working state. Dust, cigarette smoke, pet dander, environmental temperature changes, aging components, etc. can all affect a PC that is older and cause it to fail to power on if it fails its Power On Self Test (POST). Sometimes, a dustball sitting on a component can be enough to prevent the computer from booting. You need to clean that puppy out.
It's just the PC's way of telling you it needs some TLC. I noticed the issue tends to happen most when ambient temperatures start dropping....the system is colder than it has been over the summer, so it will act up occasionally upon bootup. Older components don't like being cold. Sometimes the computer is kinda flaky until I reboot it after it has warmed up a bit. It's just an old PC that really needs to be replaced or upgraded. The components do wear out over time. Yours is probably starting to do the same thing. Trust me, screwy issues will only get more frequent as time goes by. Eventually, you will be forced to replace something in the system to restore its integrity.
I'll have to admit, I've been quite lazy about cleaning out the system regularly, but I've been pretty lucky since it's been running the same format for like 4 years now. I really should re-format it just to clear out all the junk that I've filtered through it over the years, but then I come back to that whole lazy thing.....I'd rather be formatting a new rig than to just re-format the same old system and then have to hassle setting it all back up the way I had it.