I don't have a computer monitor. I've been typing all this on my iPod. I have a laptop that I might be able to hook up to but it is crashed and I don't have the cable, nor would I be able to afford it at the moment anyway.
*sigh* I guess trying to convince you people that buying something expensive just for one game when my current TV works fine with everything else is just pointless.
I think everyone gets that money is tight and that, in your mind, buying a TV for one game seems silly to you. I can relate, truly. The harsh truth remains, however, that SDTV is outdated and the Xbox is an HD gaming system, and that it says on the back of the Skyrim box what resolutions are supported. I'm sorry that you're having a rough time of it, but it's your responsibility as a consumer to pay attention to those little boxes and make an educated purchase. People with this issue are unfortunately in the minority now, and despite your claim that SDTV works "fine with everything else", there are several games just off the top of my head which say otherwise (Dead Rising, pretty much anything published by Bioware, Nier, Sacred 2, etc, etc). That you've managed to luck out and play games in which SD was considered is awesome, but understand that you're taking a gamble every time you buy one. Sadly, this time, it didn't pay off.
It svcks to have to hear, but you need to find a way to upgrade instead of expecting developers to cater to the (rapidly-growing) minority. 200 bucks seems like a lot when you're broke, I know, but it's doable in time and you'll be astonished at the difference in picture quality. Hell, hit a relative up for one for Christmas.

Check Craigslist, see if anyone you know has monitors they want to get rid of and score a VGA cable, etc, etc. Some of the folks here are trying to offer advice in a constructive manner, it's just not the advice you'd like to hear. It's not "pointless" to get with the times, but it's almost certainly pointless to expect everyone else to appease you when it's not really prudent/logical to do so, whether or not your situation is beyond your control.
Edit: Also, by your own admission, you have an Internet-capable iPod, a laptop, an Xbox, and a brand new 60 dollar game. I'm just sayin'.