Well my 1997 LS was doing something similar to turning the key and the dash lights flash, yet NO start. Actually i would turn the key, (to start mode) and only PRNDL would display. However in my case i would have to turn the key over and over a good 5-8 times for the Regal to finally START and have all the usual dash lights appear. I'm ended up changing the ignition switch.
Did u check the resistors in your fuse box?
Good luck
L.A.