If you want to have a good time, install and use Sabayon, a Gentoo
derivative, but do not take it too seriously. I screwed it up trying to install
some programs. But, for fun, it is good enough with what it has.
Otherwise, I recommend Ubuntu or PcLinuxOS or Debian or Mepis or Dreamlinux
or Aptosid or Kanotix....

I am fascinated by Arch Linux, but it is too tough for me. First of all, in
my situation, I need an easy Internet connection.

You are being very obscure in details... Tell us more please.

Could you add the output of the following info :

# emerge --info

Specify if you installed Xorg, what version, etc.

Did you read the howto about gnome ?
http://www.gentoo.org/doc/en/gnome-config.xml

I suggest you read it. There is much documentation.
And gentoo is complex to correctly install.

I used gentoo before, but now I use Funtoo. Funtoo uses more recents packages
and is more stable. Daniel Robbin, the gentoo creator, is working on Funtoo
now. But you can stick on gentoo for now it is a good distro for one that want
to learn.

Apologies for being so obscure in details. However, I am not using the same pc
as the one on which I am installing gentoo, so, did not know how to copy paste
the results. I installed xorg-x11. I have read all the documentation, and I
think its gnome howto is slightly incomplete. Anyways, I have solved the problem
somehow!!!), I read the error message more closely and it was complaining about
sqlite. So, I added sqlite and quite a few extra things in my use flags
(make.conf) and "emerge gnome" command worked. I still have to setup wireless
using wpa_supplicant, so once I get gnome desktop environment working, I will
move on to wireless.

You are right gentoo is so hard to install and definitely a great learning
curve. I hope it makes my pc faster. I guess if I have to install gentoo the
second time, it would make more sense.I have tried sending this message three
times, but it keeps on saying that the message can not be delivered. Can someone
please explain?