As pointed above, look at your "/etc/inittab", particularly the line, containing "initdefault". It must be set to 5, to start the graphical login at boot. The so called "runlevel" controls which services are started. In the file itself is usually explained briefly what the different runlevels mean. More in detail, there is several directories under "/etc/rc.d/" - "rc1.d" ... "rc6.d", containing symlinks to the startup scripts of the services. At boot, the process 1 - "init" - reads the corresponding "rc*.d " directory and executes what it finds in there. At runlevel 5, one of the services is the display manager, which shows the graphical login screen and manages the graphical sessions. Using the display manager, is, AFAIK, better way than "startx". Not long ago, I broke my KDM (KDE Display Manager), so I could "startx" from tty, but couldn't get the login screen. Some suggestions for diagnostics:
1) Check the current runlevel:
look at the last digit of the output. If it is 5, then the problem is somewhere else than in "inittab"
If it's 3 or 2, then it is normal to login at the tty. Change the "initdefault" in "/etc/inittab" to 5 and reboot, or switch to runlevel 5 manualy - as root:
# init 5
The latter is the way I prefer, since I reboot very rarely, only on power loss or when upgrading some core component like the kernel, which requires for example, reinstalling the video card driver, that can't be done with X working. I boot in runlevel 3 (Multiuser, console, with networking), make few checks, then I switch to runlevel 5.
2) If the runlevel is 5, but you don't have the login screen, try starting X maunaly, by "startx". If it works, then the problem is most probably in the display manager. If not, look at the output of the "startx" command. The problems with the X are most probably because of misconfiguration. Did you used some tool to configure X, eg. "nvidia-xconfig"?
3) Try starting the display manager manually - as root:
# xdm (the generic X display manager)
# kdm (comes with KDE)
# gdm (comes with GNOME)
The differences between them are mainly in the look and feel. While I had KDM broken, I used XDM instead (it's just more ugly
Anyway, post what you remember you did before the problem occured. Examine "/var/log/boot.log", "/var/log/messages" and especially "/var/log/prcsys.log" which is the "init" log file - look out for "[FAILED]" or something like that.