|First of all, your computer tower is not the CPU. The CPU is the processor inside the case.|
Turning on a monitor without it being connected should result in the message you see. That is normal.
No video is probably just a symptom of some problem with the computer not starting.
If your fan is running really fast the computer may be overheating. Stop trying to use it and check out things. Open the case and have a look.
Had you posted some information on your computer we might have a better idea of possible reasons for your issue. Some motherboards use a system of mounting the CPU cooler that is prone to coming loose. The system may just be extremely dusty/dirty inside and that is causing the problem. The fan is reacting to an increase in temperatures.
Did this happen all at once or have you had intermittent problems in the past?