One error message I hate to see when troubleshooting is a “No Signal” on the monitor as there are numerous events that could have caused this to happen and each one has to be checked one-by-one to find the root cause.
The cable is usually the first thing to check as it may have become loose behind the computer or the monitor. Unfortunately, some computers are in a protected podium (to prevent theft) so you will need to make sure that you can get access to the key for the lock along with having a flashlight to see in the cramped, dark space.
If the cable is connected at both ends firmly, please release them from the monitor and computer and check to see if any of the pins are bent or broken off. If tweezers cannot repair the bent pins or it is broken off, you will have to replace the cable. Be sure to check to see if it broke off in the monitor or video card port.
The integrated video card on the motherboard can go bad over time and a quick way to tell is to try known working monitor and cable. When those fail to work, try to add an aftermarket video card to the computer. If the aftermarket video card works and your computer is under warranty, quickly get the manufacturer to replace the motherboard but be warned, the motherboard will most likely be refurbished. If you are out of warranty and the repairs are more then the video card, leave it in.
Does the computer have multiple (internal and aftermarket) graphics/video cards? If so you have to tell the computer which graphics card you are planning to use in the BIOS and make sure the video cable is connected there. Some computers will force you to utilize the aftermarket card so remove the card if it will become an issue.
Does the monitor have multiple sources such as HDMI, DVI, VGA, and Display Port? If so, configure the monitor to use the correct source. Often, you can do this by the buttons on the monitor but there will be a time that the function is moved to remote control if the monitor is television.
Have you switched monitors? If you have, the screen resolution on the new monitor may be too low. If you can get access to the old monitor, use it to lower the resolution to 640×480 or 800×600 and then swap the monitors and increase the the maximum supported by the new monitor. Please not that you may need to install monitor drivers to go beyond the limit you are facing so visit the support website for the monitor to see if any are available or check in the box the monitor shipped if new.
Can you hear the power supply powering on the computer? If the computer is not on, the motherboard will not be telling the graphics/video card to send a signal to the monitor and hence the error message on the screen so be sure the monitor is connected and power on the computer.
Computers have the ability to go to sleep after a set period of time along with the monitor as well so be sure that your power settings are disabled to prevent sleep or set to a period of 4 hours or more to get you through the day.