Using 13.1, My Machine is hung on Started Accounts Service.
Starting Accounts Service...
[ok] Started Accounts Service
The System was up and running fine for months.
Any Help.
It’s probably not “hung on Started Accounts Service”, but apparently “Accounts Service” was the last service that has been started.
In the end I’d say the xdm.service, i.e. the graphical session, failed to start.
The System was up and running fine for months.
So, what did you change? 
Try to boot to “Recovery Mode” (2nd entry in “Advanced Options”).
If that works, please post the file /var/log/Xorg.0.log.old.
If not, press Ctrl+Alt+F1 and login to text mode.
Check that you have free space on your / partition.
df -h
Try to login as root, and run X via “startx”. Does that work? If not please post the error messages you get.
And it would probably be a good idea to tell which graohics card you are using and whether you installed some proprietary driver (and how).
What Desktop Environment are you using? (KDE, GNOME, …)