Using openSolaris 10 on Intel x86 hardware.

Recently I have upgraded my graphics card from Nvidia Geforce 5700 Ultra to Asus Nvidia 7600GS. For some reason the default X window manager (Gnome or Sun's version of Gnome) no longer allows me to login (after a delay I get back to the gdm prompt).

Strangely, I can login to use CDE.

On linux I can use Synaptic (debian) or Yast (Suse ) to update packages.

I am thinking that maybe a package update may cure the problem. If anyone can tell me how to update Solaris 10 or point me to documentation, it will be appreciated.

Try "updatemanager" or "smpatch" (with the update option). Those are the standard methods under the "normal" version of Solaris, perhaps they still exist in OpenSolaris too.

There is no OpenSolaris 10. It's either Solaris 10 or an OpenSolaris based distribution, like SolarisExpress (Nevada), OpenSolaris preview (Indiana), Belenix, Nexenta, MartuX or MilaX.
Update methods differs between them.
Did you try to login as a different (new) user account with no previous Gnome files ?
Solaris usual way is not to update the whole related packages but to stay in the same versions but patch the package having issues.
Indiana and Nexenta are closer to the Linux way.

Have you tried to reconfigure X with kdmconfig (xsun) or through xorg? I don't think that a patch will fix the problem. You did mention that you did change your video card. No idea why you can log into cde but not jds.