1920x1080 is not a standard resolution for PCs... it's usually 1920x1200. you may have to manually select (or even force) 1920x1080 using your graphic card's tuning app. you may also want to conifgure the card to output 1080p.
you would need to specify your pc and video card for more specific instructions.
I just had a new computer built but didn't buy a monitor as I was planning to use my 32" westinghouse sk-32h240s tv as my monitor however the desktop seems to extend past the dimensions of my tv and i've tried changing the resolution and settings but it doesn't seem to work! please help