Replying to my own post...
Got the WebPlayer booting Debian Potato (2.2 r2) off a Fujitsu 6GB laptop drive. I installed the distribution on a desktop with a CD-ROM drive and then transplanted the disk into the WebPlayer. I'm actually successfully dual-booting with WinMe using LILO, since Me supports my D-Link DSB650 and Linux doesn't (yet).
Got X working. Yes, the VGA text mode is messed up. It's really tough to use it for much of anything! Happily, XFree86 v3.3 includes support for the MediaGX graphics in Debian's xserver-svga module. I haven't tried anything other than 8bpp yet because supposedly that's all XF86 supports with the MediaGX. I used XF86Setup to get a basic config working: PS/2 mouse, high-res monitor, auto-probe SVGA chipset, 1024k video RAM, 800x600 and 8bpp. I'm not sure about the video RAM, but 1024 works... You have to use some ungodly high res monitor setting (like 1280x1024) to get the clocks for the LCD. Hopefully we'll soon have a good, tuned XF86Config file to share.
Compiled Linux 2.4.2 kernel on the WebPlayer. Took a LONG time with this slow disk and CPU. Happily, this kernel (allegedly) supports the MediaGX IDE and USB controllers and the M-Systems DoC right out of the box! We'll see how well over the next few days. The D-Link (Kawasaki) USB ethernet DID come up when I booted the new kernel, but I haven't gotten a chance to test it yet. I used the 5x86 optomizations, assuming that's appropriate for this CPU.
Compiled the M-Systems DoC driver, too. We'll see how it goes. Also compiled the M-Systems version of lilo. Beware that it needs the bin86 package (16-bit assembler) to compile... GREAT documentation in this package! Thanks, M-Systems!
Still no luck with power management. I'm using the power cord as a switch, which is not really optimal... Hopefully Linux will support enough ACPI to get it to power off.
That's all for now,