If this doesn't work, download Camtasia Studio from
www.techsmith.com, load the avi into it, make some adjustments to the video if you whish and then convert it to an animated gif file. Make sure you've enabled "tittered color reduction" and disabled "include windows colors". You'll have to test both Optimized Palette and Fixed palette and which one gives the best results; just try Optimized Palette first and see if it gives any green dots and if it does, use Fixed Palette instead.
Now open the animated gif with Image Ready (and transfer it to Photoshop if nessesary) to make some final adjustments.