My first inclination is to say that 2 megs of ram won't get you very far :D
Now that I've had my fun, I know your problem. EQ doesn't like dual cores. Luckily, all is not lost. Follow my (hopefully) easy to understand directions, and your problems will cease.
1st, start up the EQ patcher. While the patcher is running, press ctrl+alt+del and open the task manager. switch to the processes tab, and look for the eq process. Typically, it's eqgame.exe or everquest.exe, depending on how your shortcut is set up. Right-click that process, and choose Set Affinity... Pick one core or the other (which one doesn't matter particularly.) ONce you've done that, start EQ. Camp out, then re-run the patcher, go back into task manager, and check that the affinity change stayed put. If it did, voila, you're golden.
Now, for the why. Everquest doesn't know dual cores. Dual core operating systems like to move processes back and forth between the cores to get the most use out of the available processor bandwidth. Unfortunately, when EQ gets swapped back and forth, it loses its synchronization with the video card drivers. Hence the screwy animations.