This is an interesting scenario.
I actually don't see Rockefeller being a whole lot different from Ford as POTUS. I also think it makes a Rockefeller/Reagan matchup in '76 a whole lot less likely; if this had happened, the nation would have had 3 different Presidents over the span of just over 13 months. I'm not sure even the right of the GOP would have the appetite for even more instability. Moreover, had Rockefeller chosen to run (and I think under the circumstances he wouldn't have much of a choice if the alternative was Reagan), he would have had substantial personal resources to put into a campaign.
I think the main effect here might be the general election. Assume that Carter wins the Dem nomination as in OTL. The OTL '76 election was extremely close and Ford's pardon of Nixon had something to do with that. Rocky would have had to go right for Veep the same way Ford did to appease the conservatives, but wouldn't get the blame for the pardon. A good chance here that the voters, tired of a revolving door White House, stick with Rockefeller.
Here's where things get interesting. Rockefeller died of a heart attack OTL in January 1979. Presidential health care is pretty good. Perhaps his condition is discovered and he gets a bypass before the fatal heart attack? Or, alternatively, the stress of the office kills him earlier. I'll go with the latter, which gives us a new POTUS (Dole?) circa 1978. Either way, things were headed south economically starting around that time. That gives us a good chance that there is a Democrat elected in 1980, defeating whomever the GOP nominates. I think that while Reagan might at this point give the race a shot as it would be his last chance, an incumbent POTUS is going to be tough to beat in a primary. An unknown here is what's happening internationally. Are things with the USSR and Iran more or less as in OTL or different? My guess is that it's all more or less the same, though it's certainly conceivable that it could all be butterflied away by a somewhat more forceful Rockefeller posture toward the USSR and more support for the Shah. Either way, the economy still seems likely to be headed for the dumper. That, plus 12 years of the GOP, put the Democrats in a strong position.
The big question here is who do the Democrats nominate? I really don't know. The nation at this point would have been in turmoil for nearly 20 years. I'm not sure Ted Kennedy is the answer to that -- voters would be looking for stability and reassurance. Maybe he could rise to the occasion, maybe not. You might see some of the retreads of '76 try again -- it was a big field. My hunch, based on the Dem party of the era and the influence of large unions, is that Mondale might be where they turn, assuming he remained Carter's Veep pick in '76. A dark horse bet here might be Carter running again. There's no doubt he was ambitious, and he'd be one of the few Dems who'd really make the South competitive. Dems usually discard their losing candidates, but under such weird circumstances, who knows? If the '76 election was really close, his loss might be written off as a fluke of the times as voters sought stability by turning to Rocky.