Circuit breaker controls

Are you still looking for an answer to this?  It was posted before I found about Yedda, or I would have noticed it and answered sooner.  Circuit breakers and GFI switches and outlets can all malfunction and look fine and even act fine under some circumstances.  For me to pinpoint your problem, if it is still a problem, requires a little more information.  I would like to know the exact order your switches and outlets are wired in, and what test equipment you are using.

I want to run 2 20 amp circuits in a new garage. I have a 200 amp service in the house. Can I use a 10 gauge wire with ground and split it into 2 separate circuits at a sub-panel? The run will be approximately 50 feet.

Off the top of my head, I think that 10 gauge wire carrying 40 amps is about the limit.  If you want to be really safe and have a few amps to spare, you can run service cable instead of 10 gauge.  A service cable capable of carrying 60 amps isn't too awfully much more expensive than 10 gauge, is better insulated, and leaves you room for expansion in the future (when you start plugging in your electric car to charge the batteries).  Plus it will give you the ability to run 240 volts safely if need be, in case you want to use an arc welder or something else heavy duty.  It's a little more expensive, but not a lot (probably less than $20 more, if that much {this is off the top of my head and I'm not consulting texts or price lists, which is something that you should do}).