A common cause of this problem is a hard power off, which means that you have cut the power to your computer when it was still running. In this case, Puppy will prevent itself from booting to X, which will tell the user to not autostart the X server (the graphical screen) after a hard power off and will display a dialog about this and how to proceed.
If this is not the case, another possible cause would be that there is another X Server running. If your computer has halted and has not booted successfully to the graphical screen, this may seem ridiculous, because the X server has not even started a first time let alone a second time. There is a file in /tmp, named bootcnt.txt which holds information about the running graphical screen. If Puppy is shut down properly, the contents of the file are cleared. If not, Puppy checks the file during boot and sees a non-blank bootcnt.txt file and thinks the graphical screen is running and avoids starting another one. The solution is to run the command startx (or xwin) to start the graphical screen. You should get back to normal. To prevent this from happening ever again, open up your /etc/rc.d/rc.local file and add rm -f /tmp/bootcnt.txt to the end of the file.
