I have a pair of 2n5457/5458 JFETs on a small board as part of a bias scheme for a 12AX7.  The circuit also has a 9v battery.  I cannot get the voltage dialed down, so I checked the JFETs.  The resistance from gate to source (and gate to drain) read the same in both directions: roughly 1k ohm.  These are dead, aren't they?

If you are measuring out of circuit (so there is no confusion with any other parts on the board) then they are dead.  Gate to drain or source is diode-like.  Depending on the JFET, drain to source will be tens to hundreds of ohms either way around with the gate open.

Possibly a turn-on transient while the tube warms up has killed them?  Without seeing the schematic it is kind of difficult to tell for sure.

Craig, thanks for the confirmation.  I appreciate it.  They are currently in-circuit, so that could mean they are storing a charge somewhere and staying open.  I had suspected the diode-like properties had gone away, which prompted my post.  I'll remove them from the circuit for testing and if they are, indeed, burned out, I would have to replace them anyway.  

Thanks again.  

If indeed they are dead (after you get them out) you need to find out what killed them.  Post the schematic so we can have a look.