One issue I finally solved. Ubuntu 11.04 works like a charm for my desktop (1 GB DDR RAM and Pentium 4). No issues with either desktop configuration or shutdown.
However, with my Asus EeePC 1101HA, from the beginning itself there were different issues. It has 1 GB DDR2 (probably) RAM and Intel Atom processor. I had issues with the default desktop configuration (4:3) which made everything appear stretched. I had to install the Intel EMGD drivers to get a proper display, as posted earlier.
Another issue that was bugging me for sometime - after 2-3 hours of use, even if I shutdown, still it won't stop and it required me to force shutdown. I feared that it may hurt my notebook in long run.
A bit of research gave me an effective solution. Couple of simple steps and you can get rid of the bug easily. Try these steps only when the following command at the terminal doesn't work.
sudo shutdown -P now
If it works, no worries. Else, you need to try Step 1 and 2 along with the Note provided below. With these my shutdown problem is a thing of the past.
Step 1: Go to terminal and type
sudo gedit /etc/default/grub
It will open the grub file. Change the line
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash" acpi=force apm=power_off
and close it after saving.
Step 2: Again hit the terminal and type
sudo gedit /etc/modules
It will open the modules - just type apm power_off=1 below lp and save the file.
Step 3: Next type in the terminal
Now the grub will be updated and you won't face any issue with shutdown.
This works like a charm in Ubuntu 11.04 with grub2. Hopefully it will work for other versions as well.
Addition on 14Nov2011:
In addition, you may need to modify ACPI configuration to enable smooth shutdown. To do so, type the following in the terminal.
sudo modprobe -rf rt2860sta
sudo modprobe rt2860sta
echo blacklist rt2800pci | sudo tee -a /etc/modprobe.d/blacklist.conf
Once you restart your computer, your shutdown would be proper and things won't hang at shutdown.