My initial guess would be a high resistance cell in the battery. The voltage drop across the cell will vary with the amount of current required to operate different functions. Starter - very high current virtually all volts dropped, lights work but usually dimmer than normal, wipers and window motors again high current, poor or no operation.
A dirty battery post contact will have the same effect as willl a failing link betwee the battery post and the cell pack.
FWIW, from what you have said, my main guess is a failing battery..
Ken.