You can relax about the transmission, it isn’t the cause of your problem. In fact, the tranny is more than likely just as good as the day it was installed. You have problems elsewhere in the engine compartment. From the sound of your description — I would need an OBD-II scanner to prove the exact mechanical problem — I think the problem is primarily electrical or electronic. Here’s the reason: when you start a car today, there’s a short time after you key the ignition on and before it takes over that’s hardly a second or two long when you can see gauges like the thermostat or tachometer strobe quickly and then settle down. (Strobing is when a gauge swings up quickly after the circuit it is on charges up and begins communicating with the vehicle’s engine control module (ECM) which is the master computer for the motor. This is the device that collects all of the information about faults and any other statistics that the designers want monitored. If you watch closely you can see the swing up and back again as the engine settles in to run mode.) And, since you told my that the gauges jumped before your Odyssey died, I suspect that a major fault is being thrown somewhere in the ignition or charging system.
If the problem were in the transmission then you would likely be able to move the Odyssey at any time because it would go into limp-home mode. Limp-home is the manufacturer’s way of allowing your vehicle to lump on home or to a service area if the transmission has trouble or a fault is thrown indicating there is a problem somewhere in the transmission. Yes, it’s possible that even a brief system fault can make your vehicle go into limp-home. With that said, in limp-home you have at least one gear forward and, possibly, reverse, depending on the issue at hand.
Given that, the way your Honda is acting tells me that there’s a fault occurred that not only knocked your minivan out for the count, but which kept it out of action afterward. Your technician will need the OBD-II scanner to find out the problem, however, if you have some patience you will find the cause.
Like I said, from the sound of it, the problem seems to be either electrical or electronic. The electrical side of the equation means the problem could lie in the wiring or in the alternator circuitry and charging circuit. The electronic side of the equation is any of the many sensors and control modules that are used in engines today. Depending on the model, there are anywhere from eight to 27 command modules that control individual systems. They are all polled by the ECM and the results are stored in memory. The same is true of the sensors which each control module monitors.
I urge you to get your Odyssey into the shop as quickly as possible to have the problem checked out. If you use a dealership may I suggest looking for a newer used model, if you are looking for for second vehicle, using your Odyssey as a trade. Getting something newer and a bit more reliable is a good idea in your situation. The $1,200 to $2,000 that you will likely invest in finding the exact electrical/electronic fault and having it repaired seems better invested in a newer vehicle.