You can't go direct from 2010 SP3 to 2013; you will need to install the last hotfix for 2010 SP3 first.
Make sure you have the correct service pack versions (Win2008 is SP3 and SQL 2008 is SP3, SQL 2008 R2 is SP1).
Before you try an upgrade make sure you have no overlapping periods or the upgrade will hang.
Ian