One of my computers is having a power problem.

It will turn it self on without input or will not turn on, just get a power light, hard drive light and nothing else although it sounds like the hard drive is spinning as well as the power supply fan.

When it will not turn on holding the power button down will finally turn off the two lights and usually it will then boot up but again with out pressing the power on button. It will even boot with the power button disconnected from the mother board.

Hardware is 300 watt ATX power supply in a Antec case. Mother board is Abit KV7. It has two Western Digital hard drives and the normal DVD, and flopy drives.

Is this a power supply problem or a mother board problem?

When it does boot up everything works normally so I am now just leaving it on all the time.

Ah, good old electrical type problems.
If you are getting the lights, than you are getting power. You might be having two separate but related problems.

Are there other things plugged into the same switch as where the computer is plugged into? Or something else on the same run? A printer, or freezer, or dehumidifier could be a possibility.

Power supply could be going out and that is why you are getting intermittent problems. Beyond that, it may have caused a disk drive problem.
Is it at all possible to swap out the power supply and use one from another computer?

Those are the cheap ways to trouble shoot the problem. Getting a new mother board is not cheap unless you can find a used one.
That would be my last choice as to what is the cause of the problem.

Computer is plugged into a strip that has the monitor plugged into it. Nothing else. Printer is not plugged in but was connected to the computer. Wall outlet that the strip was plugged into had only a cordless phone charger connected.

Problem also occurred when computer was plugged into a different wall outlet with only a charger for the cordless phone plugged in.

Hard to tell what is plugged into other outlets on the same string. Would not be a freezer, as we don't have one and refrigerators and microwaves require a dedicated circuit. TV might be plugged in but I am not sure otherwise it is probably only table lamps.

Reading troubleshooting on the ATX power supplies shows how to check switch on the computer but nothing on self starting computers. If I read it correctly, the ATX has power on the mother board at all times, just needs the switch to close to start up.

Might just change the power supply first since that is the cheapest but if I put in a new mother board I might just go with a dual core chip.

Power problems turned out to be a failing mother board. Finally would not boot up so I changed the mother board and all is going well.