Odd computer / Monitor issue

Whenever I start up my computer occasionally it will turn on, but nothing will be on the monitor and it will not shut off unless i hit the power switch on the back of the power supply. Normally after I spend 15minutes fidgeting with the chords I can get it to turn on, but it's always something odd and random. I can eventually get both ends of them to work but always have the same issue when i turn off my PC for extended periods of time. The graphics card is new, as is the power source, so I would hope to believe that the problem lies within something else. Also if I choose to put my computer on stand-by it does not essentially "go to sleep" like it should, but rather continues to run as the monitor goes dark and once again ignores any commands from the power button and I have to visit my new best friend the power switch, which cannot be very good to be doing over and over again to my computer, or so I think. Any help is appreciated! ^_^ Ty for reading.