Thanks a lot for the replies so far. Ill be looking at all the electrical connections now. The missing information form my post is that it's a 2011 GMC Yukon Denali Hybrid, 6.0 motor, with 160,000 miles.
The transmission leak was in an o-ring, which we fixed. There may be an oil leak, but we haven't been able to drive it enough to know after we cleaned up everything form the transmission radiator leak. After we put in a new o-ring we refilled the transmission with Dexron 6 transmission fluid, and it's full and clean. THe engine oil is also full and reasonably clean after about 3,000 miles since last change.
The battery is fully charged, but does nothing when we try to start it. Thanks again for your help!