Reagan would probably defeat Bob Dole in the 1980 Republican presidential primary. If--as I am inclined to believe--by 1980 the GOP brand would be sufficiently tarnished that nobody including Reagan could save the party from defeat that year, Bob Dole might be the GOP candidate in 1984 bur he would face competition--Bush, Kemp, etc. (I don't see Elizabeth Dole as being a presidential candidate until Bob's presidential hopes are definitely finished, as they were after 1996 in OTL.)
Would Reagan even run in this timeline's 1980 election? Would he, really, run if he knew that no Republican could win, as is almost certain to be the case, in this timeline? Especially if it looked like any Republican would not only lose but, indeed, lose in a blowout. Would Reagan, really, want to be humiliated in the election? What do you think?