95 Honda Odyssey

~45k miles (with maintenence done according to miles, not time. not my choice.)
30k tune up about 2 years ago

The car cranks fine as before, but after a few seconds, the gauge cluster lights go dim and the car dies.

I'm assuming the fuel system is fine because the fuel filter is still fairly new. The only thing I can think of is the alternator, since the battery cranks just fine. The Honda dealer told us that it is probably the ignition switch.

Any tips?

 

That appears to be the alt., but the honda techs probably know more than I do.