I think playing RO without a monitor is a bit too hard to accomplish xD
I do have a friend who managed to break his laptop monitor though. So he managed to connect the computer to a TV in his room.
Depending on how old your television is, you might be able to accomplish the same with the help of the proper cables/connectors. The result probably won't be too hot, but hey, depending on how eager you are to play, it's better than not playing at all.
Here are some random links on the subject(I don't know much about it, so I can't verify how useful they really are. But I recommend researching on the matter if you're up to it
):
http://ask-leo.com/can_i_use_my_tv_as_a_...nitor.html
http://askbobrankin.com/tv_as_computer_monitor.html
http://www.answerbag.com/q_view/4384
Unfortunately, that is as much help as I can give.
edit: typo xD