Trojan.dropper found in system.exe

Yesterday Norton Internet Security found and said it fixed Trojan.dropper in system.exe.  It did so by quarantining system.exe.  A second scan found no problems.  I'm using version 19.7.1.5.  Reading about Trojan.dropper suggests that it makes a bunch of changes in the registry and leaves behind some other bad guys that pick up password entries and send them off to some distant location.  That suggests that I'm still in trouble, but neither NIS nor Microsoft's one time anti virus scanner found any further problems.  Am I still in trouble?  Should I do something to eliminate those packages left behind by Trojan.dropper and to repair the registry?