My dell PC will not turn on. Please help?

My Dell PC is about 5 years old. This happened yesterday morning, my mother turned it on and it shut off. I came downstairs to see and she was correct so what i did was unplugged everything connected to the computer and plugged it back in and boom it worked. Now today my brother tried it and it did same thing, i then proceeded to do same thing as yesterday and it did not work. I did research and it told me to take the cord that powers the PC out and try it in a home electrical appliance like a radio/light. Well i tried and the end of the cord for the light/radio did not fit into the end of the computer cord. What do i do? yesterday i did two virus checks and we did have virus's and it got rid of them cause the second one got rid of it. So it can't be a virus, so if not a virus what is it? how do i fix it? BTW: its not the outlet or power-strip because the monitor turns on. So its either computer or the cord that does not fit anything.