Here's the System Requirements for the 20" Display off Apples Tech Specs Page:
One of the following:
* Power Mac G4 or G5 with NVIDIA graphics card or ATI Radeon 7500 or better graphics card and Mac OS X v10.2.8 or later
* PowerBook G4 with DVI port and Mac OS X v10.2.8 or later
* Windows-based PCs with graphics card that supports DVI ports with full single link digital bandwidth and VESA DDC standard for plug and play setup.
So if it's still the original ATI Rage 128 Pro in your Sawtooth then yes a new Video card should fix the problem. So depending on what you want to spend, you could try to find a Radeon 7500, ATI dosen't have them for sale on their site anymore. Or for about $150 you could get a nice Radeon 9000 128MB, I've got one in my 450 AGP G4, it should have no problem driving that display. There are one or two other cards, but depending on the processor speed of your machine going more powerful than the 9000 might not help you.