No it is not possible to downgrade. You must backup and reinstall. Perhaps
you could tell us some information about your equipment and a bit about your
Linux background. 10.04 was LTS and it actaully has longer support than
10.10. Upgrades always come with risk attached, so it is best to avoid them
whenever possible. You could try to troubleshoot, but we will need some
info. Or you try a fresh installation of either 10.10 or 10.04.

I always install more than one desktop environment and it helps in
troubleshooting. If GNOME does not work then I would try installing the
package kubuntu-desktop. If it works the you could try purging
ubuntu-desktop and re-installing it from KDE. It is easier than
re-installign from scratch and takes only about ten minutes. To use
KDE/Kubuntu you just log out and change the session at the bottom to KDE or
Kubuntu. If KDE seems to drastic for you you could install xubuntu-desktop,
as it is lighter weight.