The empty SRBs would have added an additional mass to the vessel which would need to be carried into orbit until separation of the main tank. The additional fuel needed for this would mean that it would not have been possible to reach orbit.
The standard procedure for an abort between SRB separation and main-engine cut-off was the Transoceanic Abort Landing (TAL). The orbiter would have been separated from the external tank, continue on its sub-orbital trajectory and perform a landing on the designated abort runway in Europe (for every space shuttle launch, two different airports in Europe were prepared especially for this eventuality. It never happened).
Should the separation of the orbiter from the external tank also fail... well, the orbiter was unable to glide aerodynamically and land with the tank still attached, so this failure would have been catastrophic.