This is why they weren't carbed. Few beers are in that short time frame.
I'm sure your bottle capper is fine.
The
3 weeks at 70 degrees, that we recommend is the
minimum time it takes for average gravity beers to carbonate and condition. Higher grav beers take longer.
Stouts and porters have taken me between 6 and 8 weeks to carb up..
I have a 1.090 Belgian strong that took three months to carb up.
Temp and gravity are the two factors that contribute to the time it takes to carb beer. But if a beer's not ready yet, or seems low carbed, and you added the right amount of sugar to it, then it's not stalled,
it's just not time yet.
Everything you need to know about carbing and conditioning, can be found here
Of Patience and Bottle Conditioning. With emphasis on the word,
"patience." 
Lazy Llama came up with a handy dandy chart to determine how long something takes in brewing, whether it's fermentation, carbonation, bottle conditioning....
If a beer isn't carbed by "x number of weeks" you just have to give them more time. If you added your sugar, then the beer will carb up eventually, it's really a foolroof process. All beers will carb up eventually. A lot of new brewers think they have to "troubleshoot" a bottling issue, when there really is none, the beer knows how to carb itself. In fact if you run beersmiths carbing calculator, some lower grav beers don't even require additional sugar to reach their minimum level of carbonation. Just time.
