It was easier than expected. Dropped in to Radio Shack and bought 2 new, bigger capacitors for about 4 bucks total. Spent a couple of hours de-soldering, re-soldering, re-assembling and testing the fixed box.
Voila! It worked like a champ!
Learning a little about capacitors. Instead of paying 100 bucks to replace my out of warranty SlingBox I may be able to spend a buck-fifty for two capacitors and fix the dead box. Notice the two nearest capacitors have a domed top, the third capacitor in the back has a nice flat top? The dome indicates a blown capacitor. Too much pressure built up inside.