One problem related to car will not start has been reported for the 2008 Honda Odyssey. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2008 Honda Odyssey based on all problems reported for the 2008 Odyssey.
We tried to start our van early Saturday morning 6/15/13 and it was completely dead. After jumping it, we realized we hadn't left any lights on so we drove it to the nearest Honda dealership. We were told there's been a rash of this issue recently and to just make sure we turn off the air conditioner before turning off the engine and we should be okay. We drove 2 hours away from home and stayed overnight. The next morning the car didn't start again even though we had turned off the air conditioner. We bought a new battery for the car thinking it was the battery. The next weekend the car died again. This time we took it back to the dealer. They told us that the a/c compressor relay was stuck and caused the a/c system to over pressurize releasing freon into the atmosphere and discharging our battery. The dealer said that this has been a recall in other models but not our van. I feel that, although we were not in immediate danger, this should be a recall for the Odyssey and all other owners should be made aware of the issue.