Please, look beyond the monitor.
Is the PC actually booting (fans running is no guarantee of a successful boot)
When you think it should have booted, try the CAPS Lock key, every time you press it the CAPS Lock light on the keyboard should toggle off and on. If this does not happen, the problem is that the PC has not booted, so naturally the monitor cannot display anything.
If it was just the hard drive, you would still see the BIOS screen, so its probably deeper than that, based solely on your brief description. Some obscure HDD problems can prevent a boot however, and that type of failure could mean a thousand $ or more to recover the data (failed on-drive electronics).
It could be the PSU, CPU, Motherboard or ....
If you have access to another PC, I recommend removing the HDD from the failed PC and fitting it as a slave (make sure the jumper is set OK) and recover all your important files.
In this situation you will need to "take ownership" of the files and folders on the old drive to get access from the host PC, that is done as below: