What is the connection between vapor pressure and intermolecular force explanations of boiling?
Consider boiling as the rapid escape of molecules. 

In slow evaporation and in rapid boiling, only those molecules with sufficient kinetic energy are able to leave the liquid. As each "fast" molecule leaves, it subtracts its high KE from the average KE pool of the liquid, i.e. cooling it.

For evaporation to take place, there has to be a chance for molecules to escape and not to be replaced by those in the gas above the liquid. In fact, if the pressure is high (below the critical temperature), then the gas can condense to the liquid, faster than the liquid can evaporate to the gas.

For boiling to take place, there is the further restriction that localized temperature rise takes place faster than in the main body of the liquid, so that specific locations overheat, e.g. where heat flux is highest. Where pressure is a factor, then boiling may be prevented until the pressure is relieved, as in "black smokers". The water exiting the vent may be at 200 C or more, but does not boil unless the critical temperature is exceeded.