EDIT: Sorry. realised you are talking about a computer monitor, not a TV, and you don't have a remote control.
I had a similar problem, although mostly I wanted the TV to turn on automatically when I powered on the PC.
I found a product "USB Infrared Toy v2" at dangerousprototypes.com, and bought it from SeeedStudio for $22 delivered.
It plugs in to the USB port of my PC, and the infrared led on the IRToy needs to point at the front of the TV. Once you've installed the driver and software package, and updated the firmware, you can use the record utility to generate a file of the remote control power button being pressed. You can then use the playback utility to play back this file from a startup script, and it will power on the TV.


