Estimate minimum discharge voltage in a laptop battery
At 3.3~3.4V a 3.7V Lithium ion cell has practically no capacity left, and is past the 'knee' where increased current causes a large voltage drop. At this low charge state, small differences in capacity between cells also become significant, and some cells may drop their voltage before others.

In the graph below showing discharge of a typical modern 18650 cell at various currents, I have added a red dot showing where it reached 3.4V at 0.2C. At this low current the curve should be similar to open circuit - a bit lower but with a similar rapid drop. If you extrapolate and line up the discharge curves to meet at 0V then you can estimate what the voltage would be at higher current.   



But what does this mean for determining "best" 18650 cells to replace the ones in your laptop? The laptop probably refused to start because the voltage under load went below the minimum it accepts. You don't know what that cut off voltage is, but you do know that the battery had practically no charge left, so it was past the 'knee' where voltage drops rapidly. So long as your replacement cells have a similar discharge characteristic they should be OK, and the exact cutoff voltage probably isn't that important.