If you do buy a new video card, keep the current 350w psu. Try it. See if it works. If not, then replace the PSU. It "might" just work.
Also, I was under the impression that the 9800pro was capable of running the desktop at 1900x1200.
I think it might be best to create a new post in the video card forum, as some of those guys in there live and breathe video cards.
It could be that you current 9800pro is defective and is struggling to run at high resolutions, in your desktop.
Have you tried playing around with the refresh rate?
http://ati.amd.com/products/radeon9800/radeon9800pro/specs.html, it says on here it can.