south coast,
As Mad (Flt) Scientist has pointed out so well, you may have enough runway left for the "V1 of the day", and then again you may not, it depends upon whether you were Accelerate-Stop limited or not.
In the end, for the scenario that you describe, it comes down to a judgement call of whether or not the aircraft is capable of flight. If it is capable of flight, then GO! I've seen many newsreel footages of aircraft returning with doors / hatches wide open (e.g. a F28 with the forward airstairs fully down) for a fully controllable safe landing. If, on the other hand you assess that continued flight is impossible or very 'dicky' (e.g. a control jam), you now must assess the relative dangers of an overrun in a rejected takeoff, or a parlous in-flight problem.
Regards,
Old Smokey