Honestly I think you should upgrade. your specs are borderline ancient and you can build a great comp for pretty cheap right now.
As far as your problem, its probably the video card. It might not be rated to go more than 60 Hz (I have that problem).
Im not sure how your running on something with a 700MHz processor, adn 128 of RAM. (your motherboard make/model shoudl be written on the board itself, or you can use a program to get it)
Either way, I still think you should upgrade. The sad truth is that if you get a new video card, youll probably have to upgrade to a new board, which means that you will have to get a new processor, and possibly new RAM. Of course this can be good depending on how you look at it
Search the forum, there are quite a few threads about ~$1000 systems, and plenty of advice already given. but if your not sure of somethign , definitly ask!