I'm using external usb mouse on keyboard with and Debian Jessie Linux and it does not work after reboot. All I have to do is unplug and insert the mouse and keyboard again. (Reinsert) The same thing happens on two out of three totally different computers.

isa@misaThinkpad:~$ uname -a
Linux misaThinkpad 3.16-3-amd64 #1 SMP Debian 3.16.5-1 (2014-10-10) x86_64 GNU/Linux

I can simulate the reinsertion by this script

# reseting USB2 ports
for i in $(ls /sys/bus/pci/drivers/ehci-pci/|grep :)
 do echo $i >/sys/bus/pci/drivers/ehci-pci/unbind
 echo $i >/sys/bus/pci/drivers/ehci-pci/bind
done

To have it done every time I start/restart a computer I place it in a file /etc/profile.d/restart_all_usb_devices.sh so it is run automatically.

Debian Jessie uses by default systemd not SysVinit which apart from speeding up the boot process may cause your system to lock up when booting. In case you experience this problem you may prefer to keep to use older SysVinit which is also possible to use with Debian Jessie

When I have installed packages sysvinit-core systemd-shim my problem with system lock up during boot has disappeared.

Also I recommend to remove the word „quiet“ from your grub Linux boot options. You want to know what happened when your computer hangs.

More about troubleshooting Systemd can be found on debian Wiki.