First sail: stuck, no engine, coast guard

It all started out great. My wife and 5 other friends joined us to take the boat back to the Delta. We left at 9am and motored out of Vallejo and towards our destination in Iselton. We pulled up a hammock between the ketch and enjoyed the cool breeze, sounds of the waves and the peace that comes from being out on the water while sailing.
The time passed and I went to start the engine so we could get back to the doc before sunset. I was met with a gut wrenching sound of the starter trying to turn over. The batteries were drained so I shut off all the electronics and hoped the solar array would give us enough juice to start the engine. No luck. At 6pm the breeze picked up and I was confident we could at least get back to the doc before dark. The river wound around the corner and the green buoys that marked the left hand limit of the deep water channel disappeared. We were sailing in the middle of the river when we came to a gentle yet firm halt.
Swearing ensued, we attempted to get out of the mud that we were stuck on but to no avail. I hailed the coast guard at 8pm over vhf and ultimately were towed back to our doc at 1am.