Is my Kenmore HE4T Washer repairable for a reasonable price?
Everything is repairable, even a car that has been under water for years.  It's just a matter of if it's financially feasible to do so taking into account the cost of parts and labor.

My advice would be to get an opinion and quote from a few different service technicians.  If they all say that it would be cheaper to just replace the unit, then you can make your own decision as to whether you want to just replace or it attempt to fix it.

If you think it should be covered under warranty then you first need to have someone determine what is actually broken (there might be a cost to you for this which would probably be refunded if it was a warranty issue), then based on the warranty, figure out if it is covered or not.

I had a crappy washing machine in my old condo (cheap unit that the builder installed). It was going to cost $600 to fix and the same unit new was only a couple hundred dollars more.  I just bought a new (different) unit instead of trying to fix it.