Help if you can

Why would you feel the need to enter the product key after a reboot?
Maybe you can explain what you actualy did prior to entering the "product" key not production and you enter it, not install it.
Did you for instance reinstall the operating system? make and model would help as well.

After the reboot, the Microsoft office,when you open it, you have to reenter the production key.It is a Toshiba L305-S5907 Model PSLB8U-04X02F

Had you specified Microsoft office it would have been more helpful.
The Microsoft office prinstalled on your system is no doubt a trial version which has expired. You would now need to purchase it from Microsoft to get a valid key.
http://www.microsoft.com/downloads/en/default.aspx
Alternativly you can download Open Office which can much the same thing for free.
http://download.openoffice.org/