I have a lot of experience with this type of repair but little skill and no training. I suggest you go with the warranty.
I used to call my daughter "the destroyer of electronics" because she had a special gift for inducing consumer electronics to fail. Not just cheap brands but Sony, Samsung, or Apple. More than half the time it was the power connector.
Looking at the Chumby 1, I would give it a 7 out of 10 for difficulty. The bottom cover is very easy to remove (I did it jut to take a peek and to stuff the antenna inside). Unfortunately the power connector is on the top side of the board. Doing the full tear down appears straight forward ( http://www.ifixit.com/Teardown/chumby-one/1614/1 ) but I judge it not risk free.
Second point is that the power connector is surface mounted. This makes the repair easier than desoldering through-board pins but, in my experience, repairs of this type have a high chance of repeat failure. Probably this is due to my poor soldering skills and my $15 soldering iron. If I were forced to do an out of warranty repair, I would solder wires or a plug to the board and relocate the power jack so that a short length of wire provides strain relief.
I might be tempted to do the repair anyway. It would be an invitation to do other hardware modifications like the video or serial output connectors.