My computer won't turn on after being shut off until I unplug cord and plug back in! I know there are many things it could be but I will explain a little of the situation. It started about a little while ago when I came to turn the computer on. It would not start. I unplugged the computer and pressed the power button and it started. I have been doing some experimenting and found this out.
On the mobo there are three little blue lights. When I push the power button one of the blue lights will come on and not the other two and it won't start. I then unplug the cord and the blue light goes out after about 5 seconds. I plug it back in and push power and it starts. It runs fine when on.

I'm currently using a custom build computer that has a Antec case and a 350watt power supply. Thanks in advance. I really appreciate it.

You likely have a weak capacitor either in the power supply or on the motherboard. Most probably the power supply. Unplugging allows a balky capacitor to discharge.

Swap power supplies if you have another one or can borrow one.

Inspect capacitors on motherboard. Look for bulging tops (tops should be flat) or signs of electrolyte leakage. Absence of external signs does not mean that caps are good, but presence of damage means they are failing.

make sure there is no loss connection ..better try PSU before suspecting your MOBO

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