Originally Posted by FLX/MCT
"Were there any contingency scenarios in place for the case that only one booster started successfully?"
No. The maximum survivable L/R SRB ignition differential was about 100 milliseconds -- beyond that and the structure would fail.
The SRBs were originally planned for "thrust termination ports" in the nose which could be blown off and equalize the thrust allowing SRB jettison before solid fuel depletion. Later studies showed it would require 20,000 lbs of additional structural reinforcement, or about 1/3 total payload capacity, so this was dropped.
However the SRBs are best viewed as large pyrotechnic devices. The shuttle and Apollo/Saturn before it had many "criticality 1" pyros that simply had to work. E.g, the Lunar Module ascent and descent stages had no release couplings, they were cut apart with pyros, including a rocket-powered guillotine which cut through the plumbing. There was no backup; it simply had to work.
The often-stated safety measure of shutting down a liquid-fueled engine is less comprehensive than first appears. If the Saturn V had a single engine failure during the first 14 seconds of flight, thrust:weight ratio dropped below 1:1 and it would fall back onto the pad. All five engines had to work perfectly, at least that long.
The shuttle SRBs had sufficient steering authority and thrust to enable a liftoff and abort if all three SSMEs failed, however this was only possible (theoretically) after a structural upgrade in the mid-to-late 1990s.
The shuttle abort options were dramatically improved following STS-51L (Challenger) in 1986. Previously there were long "black zones" during the ascent where no abort was possible due to various structural, aerodynamic or guidance/control factors.
The contingency abort improvments can be seen in figure 7 and 8 in the 2011 AIAA document "Space Shuttle Abort Evolution"(now reproduced in the Wikipedia article Space Shuttle Abort Modes):
http://tinyurl.com/jm8zelv
The SRBs themselves were vastly improved from a reliability standpoint after Challenger. The changes were comprehensively discussed in a book by Allan J. McDonald.
Another risk of shutting down a liquid engine is the possibility of sensor-induced spurious shutdown. This happened on STS-51F in 1985 and came within seconds of a second SSME shutdown which would not have been survivable, since that was before they had bailout. A quick-thinking flight controller had them override the redline limits, which placed the SSMEs in "open loop" mode without any safety monitoring. Fortunately they made it to a low orbit; ironically that was also Challenger:
https://www.youtube.com/watch?v=0Rz82mf01Yo