question of time

I don't know how to answer the "how many licks does it take to get to the center of the Tootsie Pop" question, but you could take the scientific approach to what made that 14th game take an extra hour. Look back at the last 3 or 4 games that took appoximately the correct time and then think about the long game. Were some of the players stalling? Was is a stalemate in resources? Was it simply that dice rolls were missing what people needed to win? You can't really say there's a problem unless you can pin down what made that oddball game run so long and then you can say if it's a problem that needs to change the game.

I played a 2-hour game of Settlers one time and it was solely due to the cut-throat nature of the group I was playing with combined with timely placements of the robber and bad dice rolls. We would cut each other off as much as possible, trade very little, and the robber ended up on big numbers.

If you can't find something specific about that one game that made it run that long, it may not be a flaw but instead just a quirk of the game mixed with the people you're playing with.

As to answer how much you need to play test a game well that really depends on the type of play tests you did. Were you always present, were you always a player, or did you just sit there and watch the playtesters, or help them with the rules?
There is no definate number of times to playtest a game but you shouldn't try to make the same decisions with each play test remember your trying to break the game through your playtests try and find strange loop holes and other such things that will need changing to prevent certain outcomes or maybe even new strategies that you think need defined more so they may work. Anything that allows players more options on what they can do is a bonus in my book.
In other words the number of playtests is vastly different for every game created. Just make sure you don't always play test with the same people you need other people to try different things and different people play games differently.

how to test games at home?

And yes, testing games at home, or at game stores, or what have you. Not videogames, physical boardgames.

To find out about testing video games, you should probably post on the forums at http://www.gamedev.net, since they deal with video game development.

This forum is for board game design & development, so we wouldn't be much help in that regard.

Thanks,
-Bryk