|Monitors don't have a Safe mode - that's an operating system software feature.|
A monitor can be in a "standby" mode, when they're not receiving a video signal from the computer. The power led on the monitor is one color when it's in "standby" mode, another color when the monitor is receiving a video signal from the computer.
If your computer seems to be working properly otherwise - the power led on the computer is on, the hard drive(s) and fans spin, the hard drive activity flashes like it normally does while booting,
- if the video is fine until the computer goes into Standby or Hibernate mode, the most likely cause of the display not "waking up" when you move a mouse (that depends on ACPI settings in the bios Setup - usually moving a mouse "wakes up" the computer by default) is that you haven't loaded the main chipset drivers for the mboard, and because of that, Windows does not have the proper info about the main chipset's ACPI support - how Standby, Hibernate, and Re-Start are supported by the main chipset.
Whenever you load Windows from a regular Windows CD (or DVD) from scratch, after Setup is finished you must load the drivers for the mboard, particularly the main chipset drivers, in order for Windows to have the proper drivers for and information about your mboard hardware, including it's AGP or PCI-E, ACPI, USB 2.0 if it has it, and hard drive controller support. If you have a generic system and have the CD that came with the mboard, all the necessary drivers are on it. If you load drivers from the web, brand name system builders and mboard makers often DO NOT have the main chipset drivers listed in the downloads for your model - in that case you must go to the maker of the main chipset's web site, get the drivers, and load them.
Load the main chipset drivers first.
If your computer DOES NOT seem to be working properly otherwise, the monitor is always in "standby" mode when it's video cable is connected to a port it previously worked fine with, that indicates your monitor is probably okay, but it's not getting a video signal from your computer - in that case, then we need more descripition from you of what your symptoms are.