You can first try to follow this instruction for installing Firefox 3.x on your Linux Eee PC.
Installing Firefox 3 on the EeePC [EeeUser Eee PC Wiki]
Once FF3 is running, you may try to install zdeskop again.
Also, you may want to add this line to your ~/.profile permanently (assuming your gtk2-10 lib will be installed under the path below):
export LD_LIBRARY_PATH="/home/user/gtk2-10/usr/lib"