Hi there. I can playback DivX files on the Pentium II 333MHz at school! They're desktops, however. They have 32MB of RAM and a 8.4GB HDD. They're made by Compaq. If these POSes can play DivX, I have faith that your laptop can do it as well.
What version of the Codec are you using? At school, I use 3.11(alpha). These playback at 800x600 full screen on the supplied Compaq 15" monitors. Are you playing these back from the CDROM/DVDROM? At school, they have 8xDVDROMs which I believe are 24x CDROMs. I just pop in the CD and away I go! I'm thinking the laptop CDROM/DVDROM might be the source, but if it plays back fine when it's windowed, then it might be something else.
What version of Windows Media Player are you running? At school, we run Win95 and use WMP 6.4. I've found 7 and above to be pretty crappy. If you're using 7 and above, run a program called "mplayer2.exe". That's the 6.4 version that goes with WMP7. I've found it runs A LOT faster and much more smooth than the newer versions.
Good luck and keep us posted!