So you don't even see the POST screens that precede Windows itself starting up? Does the PC make the usual startup sounds (churning of hard drives, flashing hard disk light etc)? Could it be loading Windows as far as the Logon screen but you cannot see it? That would give credence to the monitor being the issue.
If it is stuck on the Logon screen then the mouse and keyboard would be ineffective unless you (blindly and perfectly) duplicated the normal actions to log on. I don't use a logon but if you can remember the sequence eg Enter to select default choice, type in password, hit Enter, you could try that and see if the PC continues churning.
Ruling out the monitor would be first and most certain choice.