desktop display that "streaks and stretches"

I'm a brand new Ubuntu User with serious desktop display problems.

Background:
I'm using an Inspiron 6000 (Dell); ubuntu version 8.10; the computer also still can run Windows, but Ubuntu has more than 20GB of space, so that shouldn't be the problem (or is it?). It's a fresh installation, but I checked the CD before installing. I don't know if it's relevant, but when booting Windows again, I received an error message that "das Volume ist verunreinigt" ("The volume is corrupted" (?). CHKDSK did its checks, and apparently everything is ok now.

The problem:
The desktop (including the upper toolbar) is a real mess: with stretches and streaks, pixels everywhere but where they should be (I've got a screen shot I can send if that helps). Individual windows sometimes have this problem as well, but when I maximize the window once or twice it generally goes away. When I click then again on the desktop button on the bottom left, I see the true extent of the problem, jarbled echoes of the windows I had opened. It's not impossible to work, but it's not really what I had expected.

What I've tried:
I looked at the info already in the post "display problems for 7.10", but it didn't help at all. Also tried tweeking "screen resolution", similarly to no avail.

I'd be grateful for any assistance,
Jesse