Will not stay on
Under normal circumstances, a computer monitor will not remain powered up if it is not receiving a signal from the cpu. Whether or not this is the problem in your case is difficult to say. First steps would be to check all the cable connections to the monitor and cpu, and if that doesn't solve the problem, try another monitor with your cpu to see if it truly is your monitor that is bad or if what you describe is just a symptom of a larger problem. Good luck!