Plugging the keyboard and mouse in after startup forces the drivers to load. This means the drivers either didn't load during bootup, or were unloaded for whatever reason.
Your OS install could be glitched up (possible), your HD could have some damage (more likely - run DiskFirstAid), or you have a damaged .plist preference file somewhere, that the early boot system can't handle. If the last were the case, delete some preference files.
You can check the system bootup log to see where the USB drivers should have loaded, and if they unloaded:
/Mac HD/private/var/log/system.log