faalin :
uninstall office 2013 and reinstall office 2010 then put your 2010 key in. make sure you download the correct version of office 2010 for your key.
Additional information in case:
Just to be surten,
After deinstall, restart the system before installing the nother version you want, install and restart. Sometimes it helps, don't ask me why.
Good luck and have fun doing it!