Power issues with a PC - probably defective motherboard?

Hello guys, I 've got an issue with my computer. Sometimes it will not turn on by pressing the power switch on my case and I have to turn off and back on the power switch on the back of the power supply first and only after doing that the PC will turn on.

The first time this happened I was not able to turn the PC on at all. Not even after removing the power cord for a while or by pressing the power swith on the motherboard itself. So I changed the motherboard for my old one (I was thinking the power supply is defective and wanted to test that) and it turned on just fine. I installed the original motherboard back in and now it turned on as well. But since then it has these power issues described in the first paragraph.

And it will also not wake up from sleep mode by simply pressing a key or moving a mouse like it used to. I have to press the power button on the case and then it will come on sometimes. Sometimes it will not and I have to turn off and on the power supply switch first.

The PC was working without any problems for aprox. two years. No components were added or changed recently. When I manage to turn it on it works fine and is stable, no sudden resets or anything, not even in demanding games. The mobo, cpu and memory are two years old, the PSU is 3-4 years old.

I am not sure what is the problem but I am thinking it is the motherboard. Am I right? Would replacing the internal battery on the motherboard help or it does not have to do anything with these issues?

Specs: Intel Core i5-750 2.66GHz, motherboard Gigabyte GA-P55A-UD6, 4GB DDR3 OCZ 1333MHz, PSU Thermaltake Toughpower 700W

No the internal battery is just for keeping the clock accurate.

You can check the basic functionality of the PSU by using a paperclip and shorting the GREEN wire (#14) on the motherboard harness with one of the adjacent black wires. This is exactly the same as pushing the "on" button on the case (or more accuratly the POWER header on the motherboard).

https://www.youtube.com/watch?v=2e_enZDKNAY

The PSU should be power up.

There is a standby wire on the harness (#9 - PURPLE), but I don't know how you could manually work it see if the PSU reacts to sleep mode properly.

Thank you for the tip how to test the PSU. I think however I will rather not do that now because I don't want to blow the PSU or worsen the situation somehow - the PC is working most of the time, it is just on rare occasions that it will not turn on. I wait and see how it goes and will probably have to buy a new PSU or motherboard.

what if the problem is your power button?
jump the mobo to test.

If you don't have the confidence to do at least this give up and get someone else to fix it.